Leeds held talks with Johnson and his agent last week and, after spending the weekend considering the move from Sixfields, the winger has now accepted United's offer.
Northampton will receive around £250k for the player, who was interesting as many as four other clubs and had already reportedly rejected a move to Colchester United.
The Cobblers revealed they had received two offers for the player, whose agent was criticised by Dennis Wise on Saturday when it looked as if the move was faltering.
Johnson broke in to the first team under previous Cobblers boss Colin Calderwood, but had to wait until the arrival of Stuart Gray before gaining an extended run in the team.
"We are disappointed to lose Bradley but he moves on with our best wishes and we have now got to move on ourselves," said Gray.
"I want to take this club forward but we've got a good fee for him and we didn't want to stand in his way.
"Everything I asked of Bradley he took on board and he has definitely improved as a player. He'd probably admit himself that he has been a little bit inconsistent at times this season but, credit to him, he's stuck at it and we were probably just starting to see the best of him.
"I don't want to sell any players but every player has a price and it's only maybe the top four teams in the Premier League who can afford to turn down good offers for their players."