The 27-year-old free agent, who has played in the Premier League with Reading and Burnley, is Boro boss Tony Mowbray's 12th summer signing.
Bikey-Amougou said: "I'm excited about the chance of helping Middlesbrough get back into the Premier League. The club just missed out on the play-offs last season and I can sense the ambition to go one better this year."
Mowbray added: "Andre is a player I have liked for a long time. He is a different type of centre-half to what we have got.
"He is a very powerful defender who has real physicality and he also has good technical ability. Andre hasn't played a great deal of football in the last year, but when he gets up to speed, our supporters will see the qualities he possesses."
Neymar's move from Santos to Barcelona is no doubt the biggest summer transfer.
The Nike Hypervenom is the latest cleat silo from Nike. It will change your game and is worn by the game's top players.
The USA will wear their blue away jersey against Jamaica in their World Cup qualifier on Friday night.
The hoop soccer jersey is classic and cool. The USA hooped jersey is perfect for every fan. Get in the Gear.
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
Jamaica is in need of a win against the U.S. Get the jersey of the Reggae Boyz.
England will debut their new away jersey against Brazil at the Maracana Stadium on Sunday. Get in the Gear
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
Germany is one of the top teams ever and they will play the US on Sunday.