Törnqvist was born in 1953, in Stockholm, Sweden. He has a degree from Stockholm University.
Törnqvist co-founded Gunvor in 1997, and he is its CEO.
In 2016, he reduced his stake in Gunvor from 78% to 70%, and received a special dividend of about $1 billion, part of which went to repay his co-founder Gennady Timchenko, who sold his 44% to Törnqvist in March 2014, a day before Timchenko was sanctioned by the US for his "close ties to Vladimir Putin".
In 2017, a Swedish Radio documentary presented evidence that Gunvor had been involved in a Belarusian oil smuggling scheme under Törnqvist's watch, featuring corruption at the highest levels in the Belarus government. This documentary, which includes an interview with Törnqvist, won the 2017 Prix Europa award in the "Radio Current Affairs" category. Gunvor has officially denied any wrongdoing.