Born in Copenhagen, Ellegaard spent his youth years in various Zealand clubs. In July 2002 he moved from Farum BK to Manchester City. In the 2003–04 season, he made two full appearances and two substitute appearances for the club in the league, replacing David Seaman both times when coming on as a substitute. He was loaned out to Blackpool FC for a month in January 2005, where he played two league matches in Football League One. Stuhr-Ellegaard moved to Germany to play for Hertha BSC in summer 2005. He had a hard time forcing his way into the starting line-up, and only played two Bundesliga games for the team. He moved to Danish club Randers FC as a free agentin the summer 2007. In his first half season with Randers, Ellegaard only conceded 15 goals in 18 matches. He went on to play all Randers games in his first two seasons with the club, helping Randers finish sixth in the 2007–08 and fifth in the 2008–09 Superliga season. In the 2009–10 Superliga season, Ellegaard conceded 15 goals in the first seven games, and was dropped from the starting line-up by coach John Jensen in August. As Randers' results did not improve with new goalkeeper Nathan Coe, Ellegaard was reinstated in October 2009, and only conceded eight goals in the 16-game unbeaten run that secured Randers FC another season in the top flight. Ellegaard and Randers decided to part their ways in June 2010, as they could not agree on a new contract. In season 2010–11, the Netherlands top club SC Heerenveen had big problems with their goalkeepers, so they decided that they needed to contract a new goalie for a short period. The first-keeper Brian Vandenbussche got injured during a training session, which left Heerenveen with only one goalie, Kenny Steppe. Heerenveen gave Ellegaard a trial at the club, which led to him signing a one-year contract. In the beginning, Heerenveen saw him as a second-keeper behind Steppe, but Ellegard impressed so much in training that the trainer Ron Jans made him first-choice. Despite Ellegard playing 28 matches and impressing both the audience and the trainers with his play, they decided not to renew his contract, due the fact that Vandenbussche was coming back from his injury. On 23 January 2012, Ellegaard signed a three-year contract with Swedish club IF Elfsborg as a free agent. On 24 January 2020, Ellegaard returned to Denmark and signed with Danish 2nd Division club FC Helsingør.
Denmark's best penalty keeper – Recent statistics showed that out of 29 Danish keepers, Ellegaard is the best one in saving penalties, making him a penalty specialist. He is known for his "double save" in a penalty against AFC Ajax. He had a fantastic 45% rate in penalty saves, which made him the best Danish penalty keeper.
