West Ham have agreed a transfer fee with Liverpool over the permanent transfer of Andy Carroll.
West Ham have confirmed the free-transfer signing of Romanian full-back Razvan Rat on an initial one-year deal.
Belgian defender De Laet, 23, and English midfielder James, 20, will move to the King Power Stadium on three-year contracts.
De Laet had a loan spell with Norwich last season which was terminated early in January, after previous short-term stints at Sheffield United, Preston and Portsmouth.
He made just six first-team appearances for United after a surprise move from Stoke in 2009.
Former England Under-19 captain James did not make a first-team breakthrough at Old Trafford.
He spent two loan spells at Preston in 2010 but was troubled by injury in the season just ended.
Leicester manager Nigel Pearson told his club's website: "Ritchie and Matthew are both players we have been monitoring for some time and we are very pleased to be able to bring them both to the club.
"Both are hungry, young players with winning mentalities, experience of Championship football and a desire to be successful."
De Laet told Leicester's official website: "I spoke with the manager (Nigel Pearson) and he is looking forward to the new season as much as I am. He said they want to go places and want to be at the same place I want to be, so it is a perfect match.
"It was time to move on (from United). I wanted security for my family as well. I want to settle down somewhere, find my feet and, hopefully, achieve good things. I have been out on loan a lot over the past few seasons and I think I have been just about everywhere in England.
"I went to see the stadium a few days ago and it is very impressive, and I have seen the training ground and I have been really impressed with all the facilities. Having come from United, and being on loan at Norwich as well, you come here and realise that it is a really good standard. I am really looking forward to being here every day and trying to do well for Leicester."