"Britain and Sweden have worked closely together on so many of the issues that unite us," wrote May in the article, published on Wednesday afternoon after she triggered Article 50 of the Lisbon Treaty earlier in the day. The move signalled the start of negotiations on Britain's exit from the EU.
"We want to remain committed partners and allies of Sweden and all our friends across the continent," she said.
Reiterating the points made in her speech to Britain's House of Commons, May outlined the importance of "maximum freedom" in trade between Britain, Sweden, and other EU countries and referred to a "deep and special partnership".
"Sweden is an important partner for UK business and the UK is the fourth largest EU market for Swedish goods," she noted. "It would be to the detriment of us all if unnecessary barriers to trade were erected."
As well as trade, she focused on cooperation in security, referring to the recent terrorist attack on London and calling for increased collaboration in "an increasingly unstable world."
Swedish Prime Minister Stefan Löfven had said on Wednesday that he "regrets" the UK's decision to leave the European Union but thought it was positive that negotiations can now finally begin after a "long waiting period".
Löfven also called for favourable trade relations and highlighted the need to find a "good solution for EU citizens exercising their right to settle in the UK, and vice versa" - something May did not mention in the Dagens Nyheter piece.