The €20 million (£15.7m) paid to Valencia for the 30-year-old has raised eyebrows with some but Pique, who is set to start the season alongside the Frenchman at centre-back, is firmly behind the deal.
"We needed to fill that position," the Spain international told reporters.
"Whenever Mathieu has played for Valencia in that position, he has always done well and I'm delighted with his move."
Pique, who endured a miserable summer with Spain's group-stage exit from the World Cup on the back of Barcelona's trophyless season, also commented on Xavi's stay and the departure of Cesc Fabregas.
"Despite all the rumours he was going to go, the end has not happened," the 27-year-old continued of his veteran colleague. "I've always thought that Xavi still has a part to play on the team.
"Cesc wanted to feel important and Barcelona decided to take the money. Chelsea have bought a good player."