The 49ers said in a statement announcing the trade that both players must pass a physical exam for the trade to be completed.
The Chiefs picked Baldwin 26th overall in 2011. He missed time his rookie season after getting hurt in a fight with a teammate, and has been prone to dropping passes. He has just 41 catches for 579 yards and two touchdowns in two seasons.
The 49ers picked Jenkins 30th overall last year. He appeared in only three games as a rookie and did not make a catch, even though he was healthy all season.
After another rough preseason showing against the Chiefs this past Friday night, there were questions whether the former Illinois star would even make the 49ers this season. He was targeted twice in the game, but failed to catch either pass. He had only one reception in the 49ers' preseason opener against Denver, but also lost a fumble.
"We would like to thank A.J. for his efforts as a member of the 49ers and wish him all the best with the Kansas City Chiefs," 49ers general manager Trent Baalke said in the statement. "We are pleased to add Jonathan to our team and look forward to incorporating him into our offense. Both players have been presented a great opportunity for a new beginning with their respective teams."
It's the second significant deal between the Chiefs and 49ers this year. Kansas City acquired quarterback Alex Smith from San Francisco for a pair of draft picks during the offseason.
"We felt like this trade was beneficial for all parties involved," Chiefs general manager John Dorsey said in a statement on the team's website.
"A.J. is a talented individual with a skillset that we feel can add value to our football team. Jon Baldwin is a hardworking player and a professional. We wish him nothing but the best moving forward."
Even though the Chiefs are desperate to give Smith some downfield options, Baldwin never seized upon the opportunity. He routinely dropped balls throughout training camp, and Reid and offensive coordinator Doug Pederson had seemingly grown accustomed to defending him.
"You don't know what you will get out of him," Pederson said Sunday. "If he's down from drops or mental errors or whatever it is, you just work yourself out of it. You continue to press on. We always talk about short-term memory. You have to have it in this business and move on."
The 49ers, with top receiver Michael Crabtree trying to return from a torn Achilles, are trying to solidify the position, with Anquan Boldin set to start on one side of the formation. Veteran Mario Manningham will start the season on the physically unable to perform list and will miss at least the first six games.
Information from The Associated Press was used in this report.