According to Sky Sports Italy, the 28-year-old will sign a three-year deal with AS Roma, who were crowned champions of the inaugural UEFA Europa Conference League in May this year.
Earlier on Monday, the player reportedly landed in Portugal, where Jose Mourinho's side are based for pre-season, to complete a medical ahead of his free transfer.
The Portuguese boss is said to have been a huge factor in the deal as he personally called the playmaker to explain his project in Rome in detail.
Dybala's salary at the Stadio Olimpico will reportedly be in the region of £5 million (R102 million) a year, including bonuses.
It initially seemed that Dybala would be heading to Inter Milan, but it is believed that deal fell apart when the Nerazzurri decided to re-sign striker Romelu Lukaku on loan from Chelsea earlier this month.
The Giallorossi are set to become his third club in Italy after he left Argentina to join Palermo in 2012, before making a €41 million (R713 million) switch to Juve in July 2015.
The attacking midfielder has made 271 appearances in Serie A career so far, scoring 98 goals and contributing a further 51 assists, according to Transfermarkt.