Councillors in the city voted on Thursday to have the statue removed, and to have the name of the square where it stood - named after Jankowski - changed.
They also want Jankowski stripped of the Baltic city's honorary citizenship. The city mayor has also spoken in favour of the monument's removal.
A crane took the metal figure off its stone base on Friday before a truck drove it away to a storage place.
Jankowski's critics are calling for the allegations to be examined.
The statue was funded in 2012 to recognise Jankowski's staunch support for the Solidarity pro-democracy movement in the 1980s, borne out of a strike at the Gdansk shipyard.
Questions over Jankowski resurfaced last year when at least two people alleged to Polish media that they were abused as youngsters.
A previous investigation into allegations that Jankowski sexually abused young boys was stopped in 2003.
Protesters who wanted to draw attention to the abuse allegations in strongly-Catholic Poland toppled the statue last month, cushioning its fall with car tyres. Shipyard workers had put it back up.
The monument of the late priest Henryk Jankowski is pulled down by activists in Gdansk, Poland and more photos of the day: https://t.co/Myvoh9jfIn Agencja Gazeta/Bartek Sabela pic.twitter.com/tZWif3wiFD
— Reuters Pictures (@reuterspictures) 22 February 2019
Watch: Polish Activist Topple statue of Priest Henryk Jankowski Accused of abusing children
— Montana Agent Applebutt (@_Montana_Bound_) 22 February 2019
(Video)https://t.co/9vKtRT8hhk
(Article)https://t.co/dhtjxUdjhF pic.twitter.com/AExvTmWZhd
The controversy takes place as the Vatican seeks to contain damage caused by an array of sex abuse scandals in the Catholic Church.
Jankowski, who died in 2010, gained prominence through his support for the nationwide Solidarity movement and its leader, Lech Walesa, in their struggle against Poland's communist regime.
World leaders, including former president George HW Bush and then UK prime minister Margaret Thatcher, visited Jankowski's St Brygida Church in Gdansk in recognition of his anti-communist activity.
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