The 26-year-old full-back has signed a three-and-a-half-year deal at the Reebok Stadium.
Bolton manager Gary Megson told the club's official website: "Gretar is a versatile footballer who will give us a number of options and strengthen the squad."
Steinsson himself added, "It is the right move for me.
"I am looking forward to starting work with the players and contributing to the team."
"I was here training (on trial) five-and-a-half years ago with the team and I recognise a lot of players.
"I'm just glad because I've been waiting a long time to come here.
"I was really frustrated when I didn't get a contract five-and-a-half years ago.
"I've been waiting a long time to come over and now I'm here."
Steinsson will go straight into the Wanderers squad for their away trip to Newcastle on Saturday evening.