The Serie A champions hope to unveil the player ahead of pre-season, while edging closer to signing Patrice Evra and Alvaro Morata
The Serie A champions have been in talks with both club and player since the start of July and have now struck a deal after offering €25m plus a further €2m in add-ons.
Iturbe met Verona sporting director Sean Sogliano and Juve's equivalent Fabio Paratici on Wednesday morning and expressed his desire to push through a move as swiftly as possible.
Juve are hopeful of unveiling the forward - who scored eight goals in 21 games in Serie A last term - ahead of pre-season and have also moved closer to finalising deals for two other high-profile players.
Manchester United left-back Patrice Evra is set to join the club for €3.5m on a two-year deal in the coming days, despite signing a new deal at Old Trafford earlier this summer.
The defender triggered a clause in his contract after making more than 25 appearances in 2013-14, which meant the club were obliged to offer the player an extension - something to which the 33-year-old agreed despite United's €38m capture of Southampton defender Luke Shaw.
However, the France international has now reluctantly opted to end his spell in England, with the promise of first-team football and the chance to play in the Champions League - as well as family reasons - bringing to an end his seven-year stay at Old Trafford.
Juventus will also seal the signing of Real Madrid striker Alvaro Morata, who will move to Turin in a €22m switch, which includes a straight €18m and a further €4m in add-ons.
Madrid have inserted a buy-back clause in the player's contract of €33m, which will remain in place for the first two years of his deal.
Morata is reported to have agreed a four-year deal at Juventus Stadium with the option of a further year after opting not to extend his existing deal - which ran until June 2015 - with the La Liga club.