The 24-year-old, who is trained by John Henson at City of Sheffield and Dearne Athletic Club, received the news following the British Olympic trials in Manchester.
"I’m still in shock,” he said.
"I kind of put it out of my mind and thought I wasn’t going to get picked. I talked myself into thinking I hadn’t done enough to get selected.
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"I'm really happy.”
Despite a strong season on the track, a slower-than-hoped time of 46.71 in Manchester – just over half a second behind his personal best of 46.20 – had left Lee and John waiting nervously to discover his fate.
He will now travel to Tokyo on July 15 ahead of a 10-day training camp in Yokohama, where Team GB will be based, before travelling on to the athletes’ village.
The delayed Tokyo Games will take place from Friday July 23 to Sunday August 8.
Joining Lee in the Men’s 4x400m Relay team will be Niclas Baker, Cameron Chalmers, Matthew Hudson-Smith and Michael Ohioze.
"I know them all pretty well from racing them and being on previous teams,” he said.
"It’s the same story with the women. I’m really looking forward to getting out there.”
This summer will be the first time a mixed relay event will be held at an Olympics and the GB team will be made up of athletes selected from the women’s and men’s 4x400m relay squads.
Lee, who balances a full-time career as an accountant with athletics, helped GB’s mixed relay team achieve a historic qualification in May at the World Athletics Relays in Poland.
"I just want to get out there and show what I can do in the training camp,” Lee added.
"If I get the chance to go out there and represent my country I just want to prove why I have been selected.”