Upton is making $15.45 million this season and $16.45 million next season, the final year of a five-year deal he signed with the Atlanta Braves before the 2013 season. The Padres will pay all but $5 million of what is owed to Upton, according to MLB Network and confirmed by ESPN.
Upton, 31, is in the midst of a bounce-back season after playing in only 87 games last season. A 12-year veteran, he is batting .256 with 16 home runs, 45 RBIs and a team-leading 20 stolen bases. Upton figures to provide outfield depth and versatility to the Blue Jays, who trail the first-place Baltimore Orioles by three games in the American League East.
Upton couldn't join Blue Jays general manager Ross Atkins for an early afternoon news conference, because he was at the nearest border crossing, in Buffalo, New York, being cleared to re-enter Canada.
When he arrived with the Padres on Sunday night, Upton was treated as a visitor. As a member of the Blue Jays, he requires a work visa to enter Canada.
"What attracted us to him was several things," Atkins said. "The defense at all three positions, speed, baserunning, base-stealer, power, versatility and depth."
Padres general manager A.J. Preller said the deal had been in the works for a few weeks.
"He's played well," Preller said. "He's really played both sides of the ball. He has a chance to be a 30-30 guy. He's hit some big home runs in some big spots and has played tremendous defense for us in left field."
Upton and closer Craig Kimbrel were obtained in a trade with Atlanta on the eve of Opening Day 2015. Upton missed a good deal of last season with a foot injury.
The Orioles also reportedly had expressed an interest in trading for Upton.
Upton took to Twitter on Tuesday to thank the Padres and their fans and to say he is excited to be joining the Blue Jays.
Thank you to the @Padres organization, fans and teammates for all the support and the opportunity. I enjoyed everything about my time in SD— Melvin Upton Jr. (@MelvinUptonJr) July 26, 2016
The Blue Jays currently have All-Star Michael Saunders in left field and slugger Jose Bautista in right field, meaning Upton probably will have to compete with center fielder Kevin Pillar for playing time in Toronto. The Blue Jays also could play Edwin Encarnacion more regularly at first base, opening up more at-bats at designated hitter for Saunders, Bautista and Upton.
Rodriguez, a right-hander, is 2-1 with a 3.06 ERA in six starts for Rookie League Bluefield.
Information from The Associated Press and ESPN's Jerry Crasnick contributed to this report.