Former England Under-18 international Glynn, 26, recently left relegated Bristol, having made 140 appearances for the side in total.
Lock Twomey, 25, is set to miss the start of the 2017-18 Premiership season after having further surgery on a foot injury.
"I am very excited about joining Harlequins," said Glynn.
"It is a great opportunity for me. I'm looking forward to getting stuck into the pre-season campaign with my new team-mates and hitting the ground running for when the season begins in September."
Harlequins have signed former Bristol second row Ben Glynn as cover for the injured Sam Twomey.