Lewandowski, who plays for Spanish giants Barcelona, skipped the Polish national team's June training camp and quit under former coach Michał Probierz after being stripped of the armband.
Probierz resigned on June 10, two days after a 1-2 qualifying loss to Finland.
Urban, appointed on July 16, has also brought back winger Kamil Grosicki, who had retired from international duty under Probierz.
The squad named by Urban on Friday includes three newcomers: defenders Arkadiusz Pyrka, Jan Ziółkowski and Przemysław Wiśniewski.
Poland will face the Netherlands in Rotterdam on September 4 before hosting Finland three days later at the Silesian Stadium in the southern city of Chorzów.
The squad is set to assemble on Monday for a training camp ahead of the two matches.
"I want us to begin this camp with a clean slate," Urban said in a statement on social media. "Robert Lewandowski will be the captain, and he will appear with me at a press conference on Monday.”
Urban said midfielder Piotr Zieliński has been named vice captain, with defender Jan Bednarek serving as third captain.
"The players have already been informed—I spoke with them personally and wanted them to hear my decision first," he said. "This is final, and the captaincy issue is closed. We won’t be commenting on it further."
Here is the full Poland squad for the September matches against the Netherlands and Finland:
Goalkeepers:
Bartłomiej Drągowski (Panathinaikos)
Kamil Grabara (Wolfsburg)
Bartosz Mrozek (Lech Poznań)
Łukasz Skorupski (Bologna)
Defenders:
Jan Bednarek (FC Porto)
Matty Cash (Aston Villa)
Tomasz Kędziora (PAOK Salonika)
Jakub Kiwior (Arsenal)
Arkadiusz Pyrka (St. Pauli)
Przemysław Wiśniewski (Spezia Calcio)
Paweł Wszołek (Legia Warsaw)
Jan Ziółkowski (Legia Warsaw)
Midfielders:
Przemysław Frankowski (Galatasaray)
Kamil Grosicki (Pogoń Szczecin)
Jakub Kamiński (FC Cologne)
Bartosz Kapustka (Legia Warsaw)
Jakub Piotrowski (Udinese)
Bartosz Slisz (Atlanta United)
Sebastian Szymański (Fenerbahçe)
Nicola Zalewski (Atalanta)
Piotr Zieliński (Inter Milan)
Forwards:
Adam Buksa (Udinese)
Robert Lewandowski (Barcelona)
Krzysztof Piątek (Al-Duhail)
Karol Świderski (Panathinaikos)
(gs)
Source: PAP, pzpn.pl