The deal is said to be worth in the region of £8 million and he would become West Ham's third major summer signing after midfielders Pedro Obiang from Sampdoria and Dimitri Payet from Marseille.
But what do we actually know about Ogbonna?
Well apart from the fact his picture was accidentally tweeted out by Hammers co-owner David Gold when announcing the signing of Obiang last month, not many people in England will have heard of the centre back.
Promising talent became Juventus bit-part player
The 27-year-old was an unused substitute for Juventus when they were beaten by Barcelona in the Champions League final in May.
It was a night that kind of summed up his time at the Italian champions.
Even without their first choice centre backs, Ogbonna was not trusted with a start when it mattered. He has predominantly been used at the tail end of the club's seasons when they are juggling participation domestically, in Europe and the cups and therefore rotate their squad.
He has played just 41 times, many as a sub, for Juve since signing for them in 2013.
A controversial figure who crossed the Turin divide
He is something of a controversial figure in Italy after he became the first player in history to captain Torino and transfer to hated rivals Juventus.
To put it in perspective for West Ham fans. It would be like captaining Millwall and then leaving to join West Ham, you just don't do it.
He was lucky to survive a car accident near Turin in 2008 when he ended up in a river at 5am and it will be interesting to see how he handles the bright lights of London.
As a player he has all the attributes to make him a success in the Premier League. Strong and powerful, Ogbonna is known for his outstanding physical attributes and can also play at left back.
He is good with the ball at his feet but interestingly is left footed the same as West Ham's key defender Winston Reid.
The new Joseph Yobo?
The 6ft 3in star, who is of Nigerian heritage, has 10 caps for Italy after getting citizenship on his 18th birthday.
The general consensus of opinion among Juve fans is that Ogbonna was a disappointment but that with time on his side and at a club with lower expectations and less pressure he can kickstart his career.
It is ironic that Everton were one of the other clubs in for him as he has often been likened to their famous centre back Joseph Yobo back in Nigeria due to the similarities between the two.