The move, which also affects France and Italy comes after a spate of legal challenges.
Up to now, Booking.com has not permitted hotels who use their site to charge cheaper prices elsewhere.
That was overturned following negotiations between the website and officials from France, Italy and Sweden, prompted by legal complaints from hotel trade associations. The announcement was made by the French competition authority on Tuesday.
However, hotels will still be barred from charging cheaper prices on their own website, except for customers with fidelity cards.
The changes are due to come into force on July 1st.
"We think we have found a satisfactory balance, with a win-win agreement," said Bruno Lasserre, president of the French competition commission.
However a spokesman for top French hotel trade association UMIH said the deal still did not go far enough.
"We have achieved an important step, but it does not resolve everything," said Herve Becam, vice-president of French trade association UMIH.
"We are not fully satisfied. There is still much work to do since we want an end to all parity clauses," he said.
The Local has contacted several leading Swedish hotel chains for comment.
Hotel trade associations have accused Booking.com of exploiting its dominance of the market in Europe, and the investigations were coordinated with the help of the European Commission.
Booking.com is still embroiled in negotiations in other European countries and faces legal action by France's top hotel group Accor.
Talks are also ongoing between France's competition commission and two other reservation sites, Expedia and HRS.