"Vatican authorities quickly carried out the first investigation and have established that the death was caused by natural causes," a Vatican statement said. An autopsy has been ordered and Pope Francis informed.
Wesolowski was accused of possession of child pornography and sexually abusing children during his time as papal nuncio to the Dominican Republic
His trial had to be delayed last month
when he fell ill and was rushed to a hospital in Rome.
Wesolowski, 66, was the highest-ranking Catholic official arrested for alleged sexual abuse of minors.
Link to child abuse, pedophilia
An internal church report linked him to child abuse and pedophilia, said Monsignor Agripino Nunez Collado, a Catholic University rector.
At the time, Dominican Attorney General Francisco Dominguez Brito said Wesolowski's case has various ramifications.
"Here we have to work with two legal aspects, first national laws and also international laws in his status as a diplomat, which implies other mechanisms of investigation and judgment," he said.
Test of pope's ruling
Pope Francis announced in 2013 that he was extending the court's jurisdiction in sex abuse cases to include papal diplomats, making Wesolowski's case the first test of the ruling.
He is not only charged with offenses during his five years as nuncio of the Dominican Republic, but also with child pornography charges committed in Rome between August 2013, when he was recalled, and September 2014, when he was arrested.
Pornographic images and videos
Last year, Italy's Corriere della Sera reported
that Wesolowski's laptop contained more than 100,000 files with pornographic images and videos, some showing naked teens ages 13 to 17 forced to have sexual relations with each other or with adults.
The Vatican charges also name Francisco Javier Occi Reyes, a deacon and assistant to ex-archbishop Wesolowski in the Dominican Republic, for having participated in the procurement and corruption of adolescents for the purposes of sexual abuse.
After his election to the papacy, Francis told a senior Vatican official to "act decisively" against sexual abuse and carry out "due proceedings against the guilty."
He also made it a crime to abuse children sexually or physically on Vatican grounds. The acts were already crimes under church law, but are now specifically outlawed within the Vatican city-state, which is home to hundreds of people.
Before arriving in the Dominican Republic seven years ago, Wesolowski was nuncio to Bolivia, Kazakhstan, Tajikistan, Kyrgyzstan and Uzbekistan.
He began his career as a priest in Poland in 1972, and became a bishop in 2000.