Born in Gweru in central Zimbabwe, Sweswe began his career in 2001 with CAPS United, a club based in the country's capital.
In 2004 the defender moved on again, this time to Real United in Division 1, making seven appearances and scoring only his second goal in senior football while at the club.
They had previously qualified for every CAF Champions League tournament since 2000, and won the Zimbabwe Charity Shield in 2005, but failed to win any silverware during Thomas' stay in Bulawayo.
Sweswe stayed at Dynamos for just one season before moving on to another Zimbabwean club, Mwana Africa FC, with which he reached Confederations cup quarter-finals and lost to TP Mazembe and played all the games in that tournament captaining the side.
Thomas Sweswe returned to South Africa in the 2009–10 season, signing for arguably the biggest club in his career, Kaizer Chiefs.
Prior to joining Bidvest, the defender held talks with fellow Premier Soccer League club Black Leopards but the deal eventually fell through.
In September 2012 Sweswe was ruled out for two weeks after a collision with teammate Aaron Mokoena sustained in training left the defender with deep cuts to his mouth.
He also participated in the CAF Confederations cup with Mwana Africa from a small town of Bindura in Zimbabwe they reached the quarter finals and where knocked out by TP Mazembe of DR CONGO.
Sweswe played in two of Zimbabwe's 2012 African Cup of Nations qualifiers, a 1–1 draw with Liberia on 5 September and a 0–0 stalemate with Cape Verde Islands on 10 October.
He also made appearances in two friendly matches, playing the final five minutes of the 3–0 loss to Brazil on 2 June in his first game back after injury, before helping his country to a 3–1 win over Mozambique in November.