Walsh has moved to the Milton Keynes club for an undisclosed fee, putting pen to paper on a two-year deal with the Championship newcomers.
The 23-year-old becomes Robinson’s first signing ahead of the 2015/16 campaign.
“We signed Joe on loan with the intent to make him a permanent member of the squad so I’m pleased it’s been finalised,” said Robinson.
“As I’ve said before, he gives us something we haven’t had for a while in terms of being a left-footed centre-half. He impressed us both in training and on the pitch last season and he adds to a strong group of centre-backs that we know can compete for starting places.”
Walsh said: “I’m delighted to get this deal sorted. I enjoyed my time here on loan and it just supported what I already knew – this is a club going places and I’m looking forward to being a part of it all.
“I’m really excited about playing in the Championship and I’m already itching to get back for pre-season. We’ve got a talented bunch of lads here and I’m sure he won’t just be making up the numbers.”