In November 1997, after just over a year playing in the Bundesliga he was signed by Wim Jansen for Celtic for a fee in the region of £2 million. Lambert made his debut on 8 November 1997 when he came on as a substitute in a league match at Ibrox against Rangers. Three weeks later on 30 November 1997, Lambert picked up his first winner’s medal as a Celtic player when he came on as a late substitute in Celtic’s 3–0 win over Dundee United in the Scottish League Cup Final. Thereafter, Lambert became a regular in the starting line up and scored from 25 yards in a 2–0 win over Rangers at Parkhead in the New Year game. Lambert went on to help the Scottish giants win the championship that season, their first in ten years and halted Rangers’ run of nine consecutive titles which had previously equalled the nine in a row achieved by Celtic in the Jock Stein era.
During his seven seasons with Celtic, he won four Scottish Premier League titles, two Scottish Cups, two Scottish League Cups and was Scottish Football Writer’s Player of the Year in 2002. Lambert captained the side that reached the 2003 UEFA Cup Final in Seville. Lambert’s team were drawing 2–2 after 90 minutes but after having a man sent off in extra time, conceded a third and decisive goal to José Mourinho’s Porto.