The Mets also got RHP Zack Thornton in the deal.
Taylor was drafted last season by the Pirates in the second round.
He entered the season typically ranked the 16th-best prospect in the Pirates system (Pirates Prospects, April 1).
He had a 2.57 ERA last year in 21 innings.
His fastball sits between 89-92 mph, according to online scouting reports.
Taylor, a high draftee out of Dana Hills, California, will be assigned to the Mets rookie-level Gulf Coast league affiliate.
Davis has hit .252 with a .736 OPS and four home runs in 50 games since being traded to the Pirates.