Having cost £11.8m when leaving Basel for Stamford Bridge in the summer, Veiga has made a relatively positive impact during his first six months with the Blues.
However, despite making 12 starts and six substitute outings in all competitions and becoming a full Portugal international, the 21-year-old allegedly grew frustrated at a lack of opportunities at centre-back.
Head coach Enzo Maresca recently told reporters that any player in his squad may struggle if they wish to be only used in one position, subsequently leading to constant speculation regarding Veiga's future.
Amid days of talks regarding a potential switch to Turin, Chelsea have confirmed that they have allowed Veiga to move to the Serie A giants.
What has Veiga had to say?
Juventus have moved to sign a new centre-back courtesy of Gleison Bremer suffering a serious knee injury that will keep him out for the rest of the season.
Although the expectation is that Veiga will be provided with regular appearances by Thiago Motta, Juventus possess the third-best defensive record in Italy's top flight.
Furthermore, Juventus have already qualified for the last 24 of the Champions League as a bare minimum, needing to defeat Benfica this week to have any chance of a top-eight spot in the League Phase standings.
Veiga could make his debut when Juventus play host to Empoli in Serie A on Sunday.
First of many exits for Chelsea?
With a heavily-populated squad, Chelsea are expected to facilitate a number of departures between now and the February 3 deadline.
Cesare Casadei could be next through the exit door with a move to Lazio, with reports on Monday indicated that Axel Disasi is being targeted by Aston Villa.
Ben Chilwell, Carney Chukwuemeka, Joao Felix and Christopher Nkunku are also being linked with an exit from the West Londoners.
Written by
Darren Plant