The base value of the deal is about $10.05 million, fully guaranteed. The contract includes a standard team option for a fifth year.
"Just happy to get the process over with," Richardson said.
Rookies reported Monday. Training camp begins Thursday in Cortland, N.Y.
The Jets ended up with two selections in the top 13, something that hadn't occurred since 2000. With the ninth overall choice, they picked former Alabama cornerback Dee Milliner, who remains unsigned.
The 6-foot-2, 294-pound Richardson, who played only two seasons at Missouri before opting for the draft, was the first defensive tackle picked in the draft. The Jets preferred him over two prospects that garnered more pre-draft publicity, Star Lotulelei (Carolina Panthers, 14th) and Sharrif Floyd (Minnesota Vikings, 23rd).
Richardson is expected to be an immediate starter in the Jets' 3-4 base defense. He can play any position on the line, including nose tackle, where he has lined up in some recent practices.
The Jets are building a formidable defensive line, as they used first-round picks on Muhammad Wilkerson and Quinton Coples in the 2011 and 2012 drafts, respectively. Coples is making the switch to outside linebacker, although he will be used as a lineman in certain fronts.
Richardson posted 75 tackles, 10.5 tackles for loss and four sacks last season.