Mr Hendry is now calling for changes to immigration rules.
"I am absolutely delighted that Lance Corporal Dennis Omondi will finally be reunited with his daughter," he said.
"They should never have been put through this ordeal.
"The UK government must now urgently change its restrictive immigration rules that prevent serving Commonwealth soldiers, and other Armed Forces personnel, from bringing their families to live with them in Scotland and the UK."
Prior to the decision to give LCpl Omondi's daughter a visa, the soldier's wife told Forces News the family was "heartbroken".
Speaking before confirmation that the visa would be granted, Mr Hendry led a debate in the House of Commons and said he agreed with the words of Conservative MP Tom Tugendhat that: "Commonwealth troops should be able to bring their kids to Britain - if they fight for us, they should be able to live with us."
Commonwealth troops should be able to bring their kids to Britain. If they fight for us, they should be able to live with us. https://t.co/8ZaXMX2NLb
Immigration minister Caroline Noakes said she could not comment on the specific case but insisted the Government was sympathetic and recognises the "contributions and sacrifices made by Commonwealth members of the forces".
The Army Families Federation (AFF) has said: "Commonwealth members of our Armed Forces make up a significant and vital part of the UK’s defence capability and as a nation, we ask them to make significant sacrifices to do so."