The bowler suffered a sore ankle while playing for county team Sussex last week, raising fears he would join the list of injured seamers.
England play a one-off Test against Ireland starting on June 1st, with a five-match Ashes series against Australia to follow.
The England and Wales Cricket Board said Robinson was fit enough to join up with Ben Stokes' squad for the Ireland game at Lord's.
"Scan results have revealed no damage to the ankle and that Robinson will join up with the England men's Test squad this weekend," the ECB said in a statement.
Express quick Jofra Archer has been ruled out of the entire English season with a stress fracture to his right elbow while Olly Stone is sidelined with a hamstring problem.
England great James Anderson, the most successful fast bowler in Test history with 685 wickets, is in the squad despite suffering a minor groin strain.
England captain Stokes has said he wants at least eight fit fast bowlers he can rotate during a congested Ashes schedule of five Tests in under seven weeks.
