Formerly with Derbyshire and Warwickshire, Groenewald, 32, has taken 33 Championship wickets in 2016.
Netherlands international Van der Merwe, 31, had a T20 Blast batting average of 38 this summer.
Myburgh, 35, has averaged 58.50 in three County Championship appearances this term, with a highest score of 110.
Somerset play Nottinghamshire in the final round of Championship games, starting on Tuesday, as they look to win the title for the first time in the club's history.
Somerset seam bowler Tim Groenewald, all-rounder Roelof van der Merwe and batsman Johann Myburgh have all signed extended contracts with the county.