Polish-born Wesolowski was recalled from his post as envoy to the Dominican Republic in 2013, after he was accused him of paedophilia.
In June 2014, he was found guilty by a church disciplinary panel and deemed no longer fit to serve as a priest.
The Vatican said he would stand trial on allegations of sexually abusing minors during his 2008-13 diplomatic posting to Santo Domingo.
It said he would also face charges on storing child pornography on his computer after being recalled to Rome.
The Vatican said the first hearing of the trial was scheduled for July 11.
It said Wesolowski would be the first person to be tried on the basis of anti-paedophilia laws, that Pope Francis, introduced in the Vatican Penal Code in July 2013.
It said he could face a jail sentence of up to 12 years.
The Vatican said the “serious allegations” against him were going to be scrutinised in a “delicate and detailed procedure,” using IT experts, and “if necessary” evidence supplied by judicial authorities in Santo Domingo.
Meanwhile, the Vatican said Pope Francis had accepted the resignation of the Archbishop of Saint Paul and Minneapolis, Monsignor John Clayton Nienstedt, and of his deputy, Monsignor Lee Anthony Piche.
It said the move came ten days after a U.S. attorney filed criminal charges against the Archdiocese of Saint Paul and Minneapolis for failing to protect children from a paedophile priest who was active in the area from 1997 to 2015.
Archbishop Nienstedt, in his parting statement, denied any wrongdoing.
“I leave with a clear conscience knowing that my team and I have put in place solid protocols to ensure the protection of minors and vulnerable adults.
The Catholic Church has been tarnished in recent years by worldwide revelations about paedophile priests, and by allegations that for decades its hierarchy failed to punish offenders or even covered up their crimes.
Pope Francis and his predecessor Benedict XVI have committed themselves to a “zero tolerance” policy.