Stroll was born Lawrence Sheldon Strulovitch into a Jewish family; the family name was later anglicised. His father Leo Strulović was a fashion importer who brought Pierre Cardin and Ralph Lauren clothing to Canada. Lawrence extended the Ralph Lauren brand into Europe, and together with Hong Kong investor Silas Chou, invested in American fashion labels Tommy Hilfiger and Michael Kors. The two investors played a substantial role in growing both brands to global prominence. Stroll's vehicle, Sportswear Holdings, sold its remaining stake in those businesses in 2014. During the 2000s, Chou and Stroll also invested in jeweller Asprey and Garrard.
Stroll's involvement in motorsport pre-dates his F1 ownership. From 2000 to August 2022 he owned the Circuit Mont-Tremblant racing circuit in Quebec's Laurentian Mountains. In 2014 he took ownership of the Prema Racing junior team in connection with his son Lance racing for the outfit in Formula 4 and the FIA Formula 3 European Championship. During his tenure at Prema, Stroll exerted influence over driver selection: he blocked George Russell from racing for the team in the 2014 Formula Renault 2.0 Alps Series and vetoed a planned move by Lando Norris to the team ahead of the 2018 Formula 2 season. Prema was subsequently sold to Swiss company DC Racing Solutions in 2021.
In August 2018, Stroll led a consortium of investors that purchased the assets of the defunct Force India Formula One team, which had fallen into administration. The consortium re-entered the championship mid-season 2018 as Racing Point Force India, taking seventh place in the Constructors Championship. For 2019 the team operated as Racing Point F1 Team, again finishing seventh, with Stroll's son Lance as one of the two race drivers.
On 31 January 2020, Stroll led his Yew Tree Investments consortium to invest £182 million into Aston Martin, the British luxury car manufacturer, in exchange for a 16.7 per cent stake. He became executive chairman of Aston Martin. Consistent with that investment, Racing Point F1 Team was rebranded as the Aston Martin F1 Team from the 2021 season, re-establishing the Aston Martin name in Formula One for the first time in decades.
Stroll is married to Raquel Stroll and was previously married to Belgian-born Claire-Anne Callens. He has two children from his first marriage: singer-songwriter Chloe Stroll, and racing driver Lance Stroll, who competes in Formula One for his father's team. Stroll maintains an extensive car collection that includes a 1963 Ferrari 250 GTO, a 1958 Ferrari 250 Testa Rossa, a 1967 Ferrari 330 P4, a 1996 McLaren F1, and a Ford GT. He previously owned the Ferrari dealership of Quebec. Forbes estimated his net worth at US$3.9 billion as of March 2024.