Thielen will get $35 million guaranteed, according to Ian Rapoport of NFL Media.
Thielen was entering the third season of a four-year, $19.246 million base deal, and Baratz expressed optimism in February of getting an extension worked out with the Vikings for Thielen.
Thielen, 28, has 293 receptions for 3,897 yards and 19 touchdowns in his five seasons. He topped the 1,000-yard mark each of the past two seasons and earned Pro Bowl honors both years.
Thielen caught 113 passes for 1,373 yards and nine touchdowns last season in playing all 16 games.
UPDATE 5:21 P.M.: The Vikings have announced the agreement.