The Catholic Bishops Conference of Poland announced the appointment on Sunday, the International Herald Tribune reports.
Nycz, the 57-year-old bishop of Koszalin-Kolobrzeg in northern Poland, replaces Archbishop Wielgus, who stepped down at what was meant to be his installation Mass on 7 January after admitting he cooperated with the communist-era secret police.
Speaking with Vatican Radio after the announcement, Nycz said it was a "difficult decision," but also a "gift" to take up the challenges facing the Warsaw church.
"With great and truly unhidden humility I stand before all this," he said.
Shortly after the Polish bishops announced the news, the Vatican made a brief announcement of the appointment, giving a short biography and making no mention of Wielgus.
According to the Tribune, Nycz is widely seen as holding an inscrutable record under communism. John Paul nominated him bishop of Krakow in 1988, where Nycz later organised the last three visits of the Polish-born Pope to his homeland.
Nycz said the church cannot brush over the cooperation of some priests with the communist-era secret police, but "that one must approach the issue calmly and apply the evangelical principles."
"If we don't, we are going to live from name to name, file to file, which would be very bad for the church," he added.
In 2004, John Paul named Nycz the bishop of Koszalin-Kolobrzeg diocese on the Baltic Sea coast.
Pope names Bishop Kazimierz Nycz as new archbishop of Warsaw (International Herald Tribune, 3/3/077)
LINKS (not necessarily endorsed by Church Resources)
Stanislaw Wielgus (Wikipedia)
Archdiocese of Warsaw (Polish)
Bishop Kazimierz Nycw (Catholic Hierarchy)
Benedict blesses Wielgus and encourages return to ministry (CathNews, 21/2/07)
Truth hurts, Polish bishops admit (CathNews, 15/1/07)
Russian Catholics warn against rush to judgment as Polish bishops meet (CathNews, 10/1/07)
Wielgus misled Pope by failure to disclose communist-era links: reports (CathNews, 9/1/07)
New Warsaw Archbishop resigns over collaboration allegations (CathNews, 8/1/07)
Polish Cardinal says sorry over "super spy" slur (CathNews, 15/11/06)
Polish spies in John Paul II assassination attempt (CathNews, 13/10/06)
Cardinal claims Vatican priests spied on John Paul II (CathNews, 6/9/06)
5 Mar 2007