Barr will sign a five-year, $67.5 million contract that includes $33 million guaranteed and could be worth as much as $77.5 million with incentives.
The Jets, prepared to pay Barr about $14 million per year to be an outside linebacker in their 3-4 scheme, now find themselves in need of an edge rusher.
Barr's career trajectory, and that of the Minnesota defense, appeared to be skyrocketing in 2015, when Barr was the second-highest-graded player at his position (89.6), helped the Vikings reach the playoffs while generating 27 pressures, 41 stops, an interception and two pass breakups.
The Vikings opted not to place the franchise tag on Barr.
NFL Media first reported Barr's change of heart.
Terms of the deal were not reported. However, that changed Tuesday when the Vikings increased their offer to the four-time Pro Bowl selection.
Indian diamond billionaire Nirav Modi tracked down to swanky London apartment
He has been able to operate online bank accounts in the United Kingdom while wanted by Indian authorities.... His legal team accuses the Punjab National Bank of a cover-up to avoid liability for the missing funds.
Barr was the No. 9 overall pick of Minnesota in 2014.
A nagging hamstring injury limited Barr to 13 games in 2018, his fewest since his rookie season.
The Jets - who had $82 million in cap space at the outset - then stepped up their interest in Barr.
"Thank you to the Vikings organization for giving me an opportunity to do what I love to do", Murray wrote on Instagram.
In 13 games last season, Barr had 55 tackles and three sacks.
Free agency opens Wednesday.