Poland were the first European side to crash out of the tournament in Russia in the group stage, a big disappointment after the team had reached the quarter-finals of the 2016 European Championship.
Brzeczek's contract runs until the end of 2019 and will be automatically extended if Poland qualify for Euro 2020, the country's football association said.
Speaking at his first news conference, Brzeczek, a former captain of Poland, said he realised the severity of the situation after a "difficult" World Cup in which the side's only win was a 1-0 victory over Japan after they had already been eliminated.
"I am aware of what responsibility lies with me," he said. "But I am full of enthusiasm, faith and I am available for the players so that we return to the shape they've been in before the Euros."
"Unfortunately, something went wrong at the World Cup in Russia," Brzeczek added, explaining that he was bringing in a dedicated psychologist for the team.
Asked if he wanted to rejuvenate the squad, Brzeczek said he would take small steps and keep Lewandowski, who turns 30 in August, as captain of a team that was among the oldest competing in Russia.
"Lewandowski stays on as captain," Brzeczek said. "I don't intend to carry out any revolutions. Evolution, introducing new players... but we have to do it in a cool way to keep a balance in the team."
A former midfielder, Brzeczek was part of the Poland side to win a silver medal at the 1992 Olympics in Barcelona. Since 2010, he has managed various clubs in Poland's top two domestic divisions.
(Reporting by Gabriela Baczynska; Editing by Christian Radnedge)
