Andy Burgess made his league debut for the Diamonds in the 1999/2000 season, and went on to feature in the Conference winning season in 2000/01, starting in 37 of the games that season. He then helped the team reach the playoff final in the 2001/02 season, but missed the trip to the Millennium Stadium due to suspension. He then featured for the team that won Division Three in 2003, and started in 42 games in Division Two the following season.

After more than 200 appearances for the Diamonds, Burgess left in January 2006, moving to Oxford United, but he returned to Nene Park in the summer of 2007 after making 50 appearances for the U's.

His second spell with the Diamonds lasted two season, taking him to 333 career appearances for the club, with 34 goals. At the start of the 2008/09 season he had been named as Rushden & Diamonds Club Captain, and he also assumed the role of team captain following the departure of Curtis Woodhouse.

He left the club to join his boyhood team - Luton Town - although he moved from there to Mansfield Town midway through the 2009/10 season.