A league source told ESPN's Adam Schefter that Baltimore will receive a 2020 fifth-round draft pick from Minnesota.
The trade is contingent on Vedvik passing a physical for the Vikings, the Ravens said.
Vedvik, a native of Norway, was 12-of-13 on field goals in the preseason the past two years for Baltimore after being signed as an undrafted kicker in 2018.
In Thursday's preseason opener, Vedvik increased his value by making all four of his field goals, including a 55-yarder, and had two punts over 50 yards.
"I'm really fired up for Kaare. He deserves it after everything he's been through. What an opportunity for him," Ravens special-teams coach Chris Horton said Sunday.
The trade creates a competition not only at kicker, but possibly at punter in Minnesota. Dan Bailey, the Vikings' incumbent kicker who was signed after rookie Daniel Carlson was released following three missed field goals at Green Bay in Week 2 last season, has yet to have a perfect practice in training camp.
On Wednesday, during the Vikings' final practice before their preseason opener in New Orleans, Bailey went 3-for-6 on field goals. Against the Saints, Bailey did not attempt a field goal but made all four of his point-after attempts.
Later on Sunday, ESPN confirmed an NFL Network report that the Vikings are releasing veteran long-snapper Kevin McDermott, which means rookie Austin Cutting is the team's long-snapper. Minnesota has also used several holders in camp, situationally, instead of punter Matt Wile.
McDermott's release creates about $850,000 in cap room for Minnesota, which puts the Vikings at about $5 million in cap space for the 2019 season.
Sources indicated to ESPN the Vikings want to see how Vedvik handles punting/holding duties in addition to what he could provide in the kicking game, so it not only puts Bailey's status in question, but Wile's, as well.
Minnesota coach Mike Zimmer noted some of the issues the entire kicking battery has had to work through during the first two weeks of training camp, and it pertains to the ups and downs Bailey has encountered.
"Honestly, I really like Dan Bailey," Zimmer said. "I think he's a very professional, mature kid. We've been having some issues with the snap-hold-kick kind of thing. Having two long-snappers, I think that's adding to it a little bit because the timing's different. The holding we're working on quite a bit, but I like Dan."
Four teams recently inquired about Vedvik, a source told Schefter earlier Sunday. Vedvik had made about 90% of his kicks in this year's training camp but missed a 33-yard field goal on Saturday.
In the middle of Sunday's practice, general manager Eric DeCosta spoke to coach John Harbaugh and assistant special-teams coach Randy Brown for a long time. Vedvik then left the field around 2 p.m.
Vedvik would've been traded last season, but he was assaulted in East Baltimore before the Ravens could deal him to another team. He was hospitalized in September after being found alone with multiple facial injuries. Vedvik, who had originally gone out with teammates that night, told the Ravens that he didn't remember how he ended up at the location where he was found. The Ravens placed Vedvik on the non-football injury list, which began his yearlong comeback. Baltimore had the luxury to trade Vedvik because it has Justin Tucker, the most accurate kicker in NFL history.
The Ravens have a history of being a special-teams pipeline. Three current kickers -- the New Orleans Saints' Wil Lutz, Carolina Panthers' Graham Gano and Buffalo Bills' Stephen Hauschka -- all got their starts in Baltimore. Former special-teams coach Jerry Rosburg, who retired in June, had an eye for discovering kickers, and Brown has expertise in developing talent.
ESPN's Courtney Cronin contributed to this report.