The 23-year-old defender, who left Partick at the end of last season, has agreed a two-year contract.
Hatters manager John Still told the club’s official website: “One of our scouts alerted me about Stephen – we had a look and were very impressed.
“He’s a very positive and enthusiastic player and he’s very keen to do well for himself.
“During our conversations Stephen wanted to know exactly how we saw him as a player, how we played, and wanted to know precisely the club’s future plans, on and off the pitch. He’d certainly done his homework on us.
“He was a highly sought-after player and we’re thrilled he’s joined us.”
O’Donnell joins fellow summer signings Jack Marriott, Dan Potts, Scott Cuthbert and Cameron McGeehan at Kenilworth Road.