The Bosnian bagged double figures for both goals and assists in Serie A last season and clubs have been scrambling to sign him this summer.
Chelsea and Liverpool are both long-term admirers and they were putting together proposals to lure the midfielder to England.
But they appear to have missed out to Juventus after Pjanic arrived in Turin for his medical.
The Italian champions tweeted a picture of the 26-year-old at their training base on Monday and a deal is now close to completion.
Juventus are set to pay £30million for Pjanic, while he is expected to be put to pen paper on a long-term deal.