Johnson would earn $500,000 for his fifth start, $1 million for his 10th, $500,000 for his 15th, $1 million for his 20th and $250,000 for every start from Nos. 21-33.
Johnson signed a one-year, $8 million deal with the Padres last offseason, but he missed the whole season after undergoing Tommy John surgery in April.
The Padres declined a $4 million option for 2015 this offseason, but both parties said late in the season they were interested in giving it another go.
"With Josh, he's a guy that everyone has a positive feel for," Padres general manager A.J. Preller said at the end of the regular season. "We'll try to go down the road with him and try to present something to him that makes sense to him."
The 30-year-old Johnson has been one of the game's most dominant starters when healthy. He earned All-Star nods in 2009 and '10 with the Marlins and posted a 2.30 ERA over 28 starts in '10. He was 8-14 with a 3.81 ERA in 31 starts in 2012, but made only 16 starts in 2013 for the Blue Jays because of injuries.
Video: JJ strikes out nine
He's hoping to return to form in San Diego after being unable to do so last year.
"I look at [my time in San Diego] as unfinished business," Johnson said in September. "It's been very tough to sit here and watch it all. But I think I've actually learned more this year than any other year in the past put together.
"And as far as the organization goes, I couldn't have hoped for anything better. They've been amazing. Not just the training staff, either. But everyone here ... there's been a lot of support."
Johnson started his throwing program in October and the normal Tommy John recovery period -- 12-18 months -- could mean a potential midseason return. This was his second Tommy John surgery. He underwent the first in 2007 at age 23.
Johnson is 58-45 with a 3.40 ERA in 170 games (160 starts) in nine Major League seasons.
In order to make room for Johnson on the 40-man roster, the Padres designated infielder-outfielder Jake Goebbert for assignment. Goebbert hit .218 in 51 games with the Padres after joining the team in a trade from the A's on May 15 -- a deal that sent Kyle Blanks to Oakland.