The 23-year-old, who joined the Trotters from Vasas SC in August 2007, made his first-team debut in the Carling Cup win over Southampton in August and has gone on to make seven further appearances, including three in the Barclays Premier League.
Bolton boss Owen Coyle said: "We're delighted that Adam's committed himself to a new contract. It shows that we're investing in young players and trying to build the football club with that nucleus of those young players."
He added: "Mark Davies, Fabrice Muamba and Lee Chung-yong have all committed themselves to new deals at the club and Adam's the same.
"Since I came to the football club he's been outstanding and to have a young goalkeeper of that ilk commit himself is great news for everybody."
Bogdan has been working with, and now providing competition for, Bolton's long-serving number one Jussi Jaaskelainen, who turns 36 next month.
Coyle added: "Jussi has probably been one of, if not the, top performers in the Barclays Premier League for the last 10 years and for Adam to work with someone of that quality, it can only help him. And Jussi knows he's now got real competition."
Source: PA
Source: PA