The 18-year-old impressed during a stint last year and a deal to take him from Waitakere United was agreed.
He has now flown into the UK to begin his career with Rovers on an initial two-and-half-year deal, and he is in line to feature for the club's reserve side next week.
Rovers defender and countryman Ryan Nelsen played a part in getting Payne to Ewood Park but insisted that the teenager very much earned the move.
"He has done really well and it has all been on Tim's back," said Nelsen.
"Sure, I have got him the opportunity there but they are not giving him a contract because of me.
"He had to play well, plain and simple, and they have watched him a lot."