The Old Lady were among a host of Serie A clubs supposedly interested in the Danish striker and appear to have pipped AC Milan for his signature.
Juventus have agreed to take Bendtner, who was deemed surplus to requirements by Gunners boss Arsene Wenger, on an initial season-long loan with the option to buy him for around £5m.
The 24-year-old tweeted: "So happy and humble. A dream come true."
Bendtner spent last campaign on loan at Sunderland but neither party was eager to make the transfer permanent.