''I honestly can't grasp the fact that we've been able to accomplish all of this,'' Vinci said. ''I think I'll realize it all after we finish playing. I'll say, 'Wow, we did all of that.'''
It's the fifth major championship for Errani and Vinci, with at least one at each Grand Slam tournament. The first came at the French Open in 2012, followed by the U.S. Open later that year, and the Australian Open in 2013 and 2014.
Asked to compare this trophy to their previous four, Errani replied: ''It's different because it's the (career) Grand Slam. I thought about it all day. Even on court, during the match, I thought about it. It's something historic.''
According to the WTA, the four other partnerships with career Slams in women's doubles are Serena and Venus Williams; Martina Navratilova and Pam Shriver; Gigi Fernandez and Natasha Zvereva; and Kathy Jordan and Anne Smith.
She and Vinci fell to the ground and hugged after winning under the closed roof at Centre Court. Later, they completed each other's sentences while answering questions in Italian from reporters.
''I don't think I ever was as tense as I was today. Not even singles,'' said Errani, the 2012 French Open runner-up. ''I was thinking about the Grand Slam. It's crazy.''
They were playing in their eighth major final, and Errani said their friendship off the court made them better competitors on it.
Babos and Mladenovic were making their debut as a team in a Grand Slam tournament. They had six double-faults and were broken five times.
Mladenovic won last year's mixed doubles title with Canada's Daniel Nestor; Babos won the 2010 Wimbledon girls' doubles title.