Burchert began his career with Wartenberger SV. In summer 2002, he was scouted by Hertha BSC. He signed his first professional contract on 30 January 2008. Burchert made his Hertha debut on 17 September 2009 in an Europa League match against Latvian side, FK Ventspils and came on in the twenty-first minute replacing starting goalkeeper Jaroslav Drobný.
Burchert played his first Bundesliga game on 20 September 2009 against SC Freiburg. In his second game Burchert conceded two strange goals. Having replaced the injured Timo Ochs with the score at 1–1, Burchert was caught off his line having headed a clearance from a through ball, with Hamburg's David Jarolím volleying the ball into an empty net from long range. Two minutes later the same thing happened, with Zé Roberto scoring from the edge of the centre circle with Burchert off his line following another headed clearance.