The North Yorkshire base – which provides a continuous ballistic missile early warning service to the UK and US - projected images of the NHS fundraising hero onto the surface of its pyramid structure radar.
Captain Sir Tom captured the hearts of the nation with his fundraising efforts during the first lockdown when he walked 100 laps of his garden ahead of his 100th birthday last year, raising more than £32m for the NHS.
The national hero and Second World War veteran from Keighley in West Yorkshire died at Bedford Hospital on 2 February, after testing positive for COVID-19.
It took five projectors beaming 52,000 lumens across 180m to cast Captain Sir Tom's image onto the 33m-high radar.
Wing Commander Al Walton, Station Commander at Fylingdales, explained the significance of the tribute.
He said: "He's an iconic Yorkshire man, he's captured the nation's heart, he's a very proud military man and we thought 'what better iconic military place in Yorkshire to do it than on the SSPAR [Solid State Phased Array Radar] radar in Fylingdales?'.
"The image of him... in his dinner jacket or with the walker, I think, probably will be the defining image of the COVID pandemic."
Wing Cdr Walton also spoke about how Captain Sir Tom's actions represented the best of the military's ideals.
"You can take people out of the military but you can’t take the military out of the people," he said.
"A lot of us join up for selfless reasons to do what we can for the nation and for Queen and country, or King and country as it would have been in his time.
"I think that really resonates with a lot people in the military – it gives you an idea that there's something bigger than just yourself as you go through either troubled times, be it in conflict or in peacetime with issues that we have at the moment."
Representatives of the Armed Forces will perform ceremonial duties at Captain Sir Tom's funeral on Saturday in recognition of his service in the Army and close links to the military.
It has been described as a "small family funeral" and in line with current COVID-19 restrictions, it will be attended by eight members of Captain Sir Tom's immediate family; his two daughters, four grandchildren and both sons-in-law.
His family has requested the public not to attend and have set up an online book of condolence and suggested people either plant a tree in his memory or donate to The Captain Tom Foundation or a charity of their choice.