"I have to start by doing what good manners require, which is to congratulate the victor" the BBC quoted Kaczynski as telling his supporters.
Kaczynski, representing the far-right Law and Justice Party, had sought to fill the vacancy created when his twin brother, President Lech Kaczynski, died in an April plane crash with 94 others in Russia.
The BBC reported Komorowski, the speaker of parliament, acting president and leader of the ruling Civic Platform party, had received 52.6 percent of the vote and Kaczynski had 47.4 percent.
Komorowski's supporters withheld a declaration of victory pending the release of official results, the British network said.
Final results were not expected to be announced by the electoral commission until Monday afternoon.
Still, Komorowski appeared optimistic, the BBC said.
"Tonight we will open a small bottle of champagne and tomorrow we will open a big bottle," he said.
"We thank everybody -- the more so that it was an unusual campaign, a difficult campaign held in the shadow of catastrophe."
Martin Bashir resigns from MSNBC over Sarah Palin comments
Ron Burgundy interviews Peyton Manning on SportsCenter