The midfielder has signed a two-and-a-half year deal at Elland Road.
The former Watford man was also attracting interest from Scottish Championship leaders Rangers (via STV), but Evans claimed that the Whites had beaten Mark Warburton's men to his signature, before explaining how delighted he was to get the deal done.
"He's signed this morning," Evans told STV.
"It's taken a little while to get there but I'm delighted we've got there. I'm grateful to the owner Mr Cellino who's made this happen.
"I wanted to build. I thought we wouldn't get there so I was pleased to get it over the line. He was up there with my top targets."
It is no surprise that Evans was keen on the powerful midfielder, as he also suggested that Diarouraga reminds him of former Arsenal and Manchester City great Patrick Vieira.
"We've got a boy who's 6 foot 2, we've got a Patrick Vieira-type player," he added. "He brings real quality to our midfield."
The deal is a major boost for Leeds as they look to get back to winning ways, having suffered successive defeats to Ipswich and Sheffield Wednesday.
The two losses have left the Whites 13 points adrift of the play-off places, and Evans will be hoping that Diagouraga's presence will inspire the rest of the side to start clawing back the gap to the Championship's top six.