The speedy 18-year-old has made 14 substitute appearances for The Robins' first team this season, scoring four goals in the process.
Lita has been a regular in the West Country club's reserves as well and was still on trainee forms with the club until this weekend.
On his first pro contract, Lita told Bristol City Radio: "I am delighted to have signed, it's been a while in coming.
"I don't have to worry about it now, I can concentrate fully on my football.
"I know I'm going to be here for the next three years now and I'll be doing my best for this club and hopefully break into the first team.
"The manager and chairman obviously believe in me, now it's my turn to go out there and show what I can do."
Meanwhile, midfielder Ben Cleverley has extended his loan with Conference side Forest Green Rovers for a second month.
The youngster has been unable to feature much for the Gloucestershire non-leaguers, after he picked up an ankle injury on Boxing Day.
However, Cleverley has returned fit and with Forest Green keen to extend his loan, Robins boss Danny Wilson was happy to grant their request.
"It is great for Ben to get regular first team football, it's much better than playing reserve team football," Wilson told the club's official website.
"It is a higher standard of football, it's very tough and it will get players like Ben ready if they are ever needed for first team football at Ashton Gate."
