The trade was confirmed by Hicks' agent, Frank Murtha, and Hoomanawanui's agent, Rick Smith.
Hicks, a third-round draft choice by New Orleans in 2012, has been a starter since 2013 and was at Saints practice Wednesday.
Recently, however, Saints coach Sean Payton has trimmed Hicks' playing time, saying production on the interior defensive line improved by rotating in other players. Payton also has said this week that he's concerned about New Orleans' depth at tight end.
Hoomanawanui, who has played for New England since 2012, began his NFL career as a fifth-round draft pick by St. Louis in 2010.
Hoomanawanui started 12 games for New England last season, making three catches. He's played in two games as a reserve this season without a catch.
The Boston Globe and NFL.com initially reported different parts of the deal.
In New Orleans, the trade could result in Bobby Richardson, an undrafted rookie out of Indiana, being moved into the starting lineup. The Saints' efforts to get Richardson into games had already cut into Hicks' playing time during the previous two games.
Hoomanawanui, will join a tight end group in New Orleans that before the trade included only two players on the active roster, former Patriot Ben Watson and third-year pro Josh Hill.
Just hours before the trade, Payton, in discussing the roster, told reporters, "We're still short at tight end, and that's an area that concerns me."
Now that appears to have been addressed, with Hoomanawanui joining cornerback Brandon Browner as members of the Saints who won a championship with New England last season.
The Saints (0-3) host Dallas on Sunday night, and the Patriots (3-0) have a bye this week.
The 6-foot-5, 324-pound Hicks, who has been listed as both a tackle and an end with New Orleans, had his best season in 2013, when he had 4 1/2 sacks. Last season, he had two sacks and this season has not recorded any while assisting on two tackles.
Last week, Hicks sounded bothered by his role in New Orleans' defence this season, saying he was "benched" during a Week 2 loss to Tampa Bay.
When Payton was asked about Hicks' comments, he responded, "Rotating a defensive lineman is pretty common. Now if he felt like he was benched, then, hey. But after we did that, we had pretty good production defensively — in fact, very good."
Hicks, a California native, was a coveted LSU recruit, but was dismissed from school because he'd received impermissible housing and other assistance from an assistant coach who resigned over the matter. Hicks then played college football in Canada before turning pro.
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