Born in Stockholm, Bergqvist moved with his family to England when he was seven years old.[2] He played youth football with Reading and Queens Park Rangers, before joining Aldershot Town in 2009.[3] Bergqvist eventually became youth team captain at Aldershot,[4] and spent loan spells at both Thatcham Town and Dorchester Town,[5] before making his senior debut for Aldershot in May 2011.[6] He joined Farnborough on loan in August 2011,[7] and Basingstoke Town in October 2012.[8]
Bergqvist signed for Exeter City in June 2013,[9] before moving on loan to Welling United a few days later, for the whole of the 2013–14 season.[10][11]
On 10 February 2014, Bergqvist left England to return to Sweden, signing a two-year contract with Östersund on a free transfer.[12] He did so as part of a scheme called 'League Football Education' which aims to obtain contracts abroad for players in the English league system, alongside Andrew Mills and Jamie Hopcutt.[13]
On 27 March 2019, Bergqvist joined Eliteserien side Haugesund on loan until 31 July with an option to make the deal permanent.[14]