"We have lost the election," Mr Persson told his Social Democratic Party supporters in Stockholm.
Mr Persson, who has headed a minority government since 1996, also announced his resignation as party leader.
Mr Reinfeldt, who heads the four-party Alliance for Sweden, meanwhile claimed victory in a speech to his conservative Moderate Party supporters.
"We ran in the election as the New Moderates, we have won the election as the New Moderates and we will also together with our Alliance friends govern Sweden as the New Moderates," Mr Reinfeldt said.
Mr Reinfeldt is seen as having breathed new life into the opposition by uniting the notoriously divided bloc, after having shifted his own conservative Moderate Party toward the middle to create the New Moderates.
The party was expected to register one of its best election scores ever, with estimates predicting it would garner 25.1 percent of voter sympathies compared to 15.2 percent in 2002 elections.
The Alliance has vowed to slash income taxes for low income earners and improve the business climate for small and medium-sized companies, all the while pouring more money into Swedes' cherished welfare state.