The 24-year-old arrived at the Clayton Wood Training Ground on Wednesday morning to finalise his season-long loan switch from Portuguese giants FC Porto.
The terms of the agreement also include an option for the Potters to make the deal permanent at the end of the 2016/17 campaign.
Announcing the news, Chief Executive Tony Scholes said: "It's been a productive day for us having managed to get three important deals over the line.
"We set out to address several areas of the squad that Mark Hughes felt needed looking at this summer, and we are delighted that we have been able to do that.
"Bruno is a player that the manager has admired for quite some time and as soon as the opportunity arose for us to make this deal happen, we reacted quickly to make sure we could conclude it."
Manager Mark Hughes was equally as delighted to have acquired the services of the pacey and powerful central defender.
"We have been aware of Bruno for quite some time now, as many other clubs around Europe have been," the Welshman said.
"He is a very accomplished defender who has a lot of experience at a very high level, including playing for Holland during their good run at the 2014 World Cup.
"He is a guy that we feel can come in and make an immediate impression, because he boasts all the attributes needed to perform at the top level of the Premier League."