The Sky Bet League One have been publicly searching for someone to assume control from the 74-year-old, who claims Rovers need new investment to take them forward.
Johnson is satisfied he has now found the perfect buyer and, barring a late hitch, expects the formalities to be completed swiftly.
"I had to find somebody who loves the club and who the fans can trust," he said in an interview with BBC Late Kick Off.
"I think I've done that now. We expect to make an announcement fairly soon - in a couple of weeks.
"There's many a slip twixt cup and lip and you never know until the ink's dry. (But) I'm quite confident that it's happening."
Last month Michael Wilde, the former chairman of Southampton, pulled out of the running with a bid which would have seen ex-Chelsea defender Albert Ferrer installed as the club's new manager.
The Tranmere Rovers Trust also launched a campaign to try and buy the club themselves but are unlikely to raise the funds needed, according to Johnson.
"It does need money, unfortunately it needs a lot of money," he added.
"We're one of the poorer clubs and our wage bill is quite low compared to some of the clubs in both our division and the division below.
"They (the prospective new owner) are a bit younger than I am. They've got the money and I'm satisfied the fans will be able to trust them."
Assistant manager John McMahon, standing in following Ronnie Moore's suspension, admits the uncertainty over the club's future has left him with little scope to plan beyond this season.
"I think it will be positive if the deal does go through," he said.
"The chairman has been absolutely fantastic for this football club and he deserves a lot of credit for what he's done - both financially and in terms of backing people."