Steinsson will earn £15,000-a-week, just four years after living in a garage while playing for BSC Young Boys.
Megson said: "He's a quality right-back and he certainly hasn't been born with a silver spoon in his mouth.
"He comes from a place in Iceland with just 800 people. But he wanted to be a footballer and did everything to make sure he became one.
"He took himself off to Switzerland and lived in a garage and that shows he has a fantastic attitude.
"He is a good athlete, good in the air, decent on the ball and will help us improve."
Bolton could have saved themselves a fortune by taking Steinsson on a free transfer five years ago.
The defender failed to impress whilst on trial at the Reebok, but has been monitored ever since.