New England waited out six full rounds of the league's annual three-day selection process before adding to the quarterback room.
Etling, who transferred to LSU after two seasons at Purdue, experienced his share of ups and down on his collegiate career.
After sitting out the 2015 season because of NCAA transfer rules, Etling completed 325 of 544 passes for a 59.7 completion percentage in two seasons in Baton Rouge (2016-17). He threw for 4,586 yards and 27 touchdowns against seven interceptions.
While at Purdue from 2013 to 2014, Etling completed 238 of 429 passes (55.5 percent) for 2,490 yards and 16 touchdowns against 12 interceptions.