The soldier killed in Syria on Thursday has been named as Sergeant Matt Tonroe from the 3rd Battalion the Parachute Regiment.
The MOD said he was "tragically killed in action whilst on duty" in Syria while on an anti-Islamic State operation.
A US soldier was also killed and five others wounded on Thursday by a roadside bomb, the US military said.
A statement released by the MOD reads:
"Sergeant Tonroe was born in Manchester on the 14th of August 1984.
"He enlisted in the Army on the 27th September 2004. On completion of his initial training, he joined the 3rd Battalion of The Parachute Regiment in Colchester where he served as part of the Sniper Platoon.
"He rapidly developed an array of competencies and combat experiences that were to lay the foundations of an outstanding career.
"During his service, Matt deployed numerous times on operations to Afghanistan and the Middle East.
"His distinguished service reflected a man that was happiest when professionally tested on operations.
"He relished responsibility, the opportunity to contribute and when the time came, to lead.
"He was a natural in this role.
"Matt was also a capable and respected parachutist. As a gifted instructor he was free with his time and his advice, and would dedicate himself to support and develop this skill in others.
"He was well known within his unit, well-liked by all and he will be sorely missed. When talking of Matt, his colleagues recount his humour, mischief and endless endeavours.
"Laid back, but a consummate professional, Matt was utterly selfless and always strived to achieve excellence.
"Matt was very much a family man, making every effort to see him beloved mum around numerous overseas deployments.
"He is survived by his mother Michelle, his brother Alex and girlfriend Olivia."
Sgt Tonroe’s Officer Commanding said: "If you had met Matt Tonroe, then you would have liked him.
"He bristled with the contentment of a life lived to its full.
"His bravery and talent as a soldier, was matched by his compassion as a human being.
"He was an individual, with the courage to set his own course, and the perspective to see new possibilities at every turn.
"He was destined for great things in our unit; his leadership was both natural and apparently effortless.
"He is already missed. Without Matt, our company has lost some of its humour; some of its warmth; and some of its sheer opportunism.
"We will always remember him."
Sgt Tonroe’s Commanding Officer said: "Matt Tonroe was a deeply intelligent man and one of life’s characters.
"He was a caring and considerate soul, a loving and dutiful son, and a friend to many.
"Yet he had a steel core, served his country with pride and was a first class soldier, proven in combat, faced risk willingly and was ever ready for more.
"He thus died as he lived: daring and fearless in duty.
"We mourn his loss dearly, are proud to have known him and will honour him by continuing this fight."
Defence Secretary Gavin Williamson said: "My thoughts and prayers are with the family and friends of Sergeant Matt Tonroe at this dreadful time.
"Sergeant Tonroe served his country with great distinction and it is clear from the tributes made by his colleagues that he was not only exceptionally dedicated and courageous but also a gifted and intelligent instructor who was respected by everyone he served with.
"Sergeant Tonroe fought to protect British values, our freedoms and to keep us back at home safe.
"His sacrifice, unflinching commitment and bravery will never be forgotten."
The news that a UK Armed Forces member had been killed in Syria was announced yesterday by a MOD spokesperson:
“It is with regret that we must confirm that a member of the UK Armed Forces was killed by an improvised explosive device in Syria yesterday.
“The individual was embedded with US forces on a counter-Daesh operation when the incident occurred.
“The family has been notified and our thoughts are with them at this difficult time.
“We cannot confirm any further details at this stage.”
The government has never said publicly that UK forces are in Syria. It is also reportedly the first British military death whilst on deployment against IS.
The US military member killed was the fourth American who has died in Syria since the US began attacking Islamic State militants there in September 2014, according to the Pentagon's Defence Casualty Analysis System.
Of the three previous deaths, Air Force Staff Sergeant Austin Bieren was specifically labelled by the Pentagon as a non-combat death.
Another, Navy Senior Chief Petty Officer Scott C. Dayton, was killed by an improved explosive device.
The third, Army Specialist Etienne J. Murphy, died in a vehicle rollover.
The MOD did not say where the incident occurred but it came hours after a local Syrian official said that a roadside bomb exploded in the tense, mixed Arab-Kurdish town of Manbij that is not far from the border with Turkey.
Manbij is under threat from a Turkish military operation. Ankara says Syrian Kurdish militiamen it views as "terrorists" and an extension of Kurdish insurgents inside Turkey are in control of the town.
A US military statement released on Friday afternoon said the attack happened on Thursday night and that the wounded were being evacuated for further medical treatment.
US military spokesman Col Ryan Dillon could not immediately say who was behind the attack:
"There is an investigation underway to identify who they could possibly be. We have our initial assessment and thoughts on that but we won't provide until the investigation is complete."
Col Dillon said the coalition has had fatalities in Syria before: "Perhaps by different means but there have been coalition deaths in Syria over the course of three years."
Mohammed Abu Adel, head of the Manbij Military Council, an Arab-Kurdish group in the town backed by the US, said the bomb went off hundreds of metres from a security headquarters that houses the council just before midnight on Thursday.
Earlier on Friday, Col Dillon said an incident involving coalition forces was reported in Manbij but said no more information was available.
The town has seen a number of small explosions, protests and an assassination attempt on a member of the Manbij military council in recent weeks.
The military council has since been in control and US troops patrol the town and area with troops based nearby.