The much-maligned Wayne Hunter will be sent to the Rams to complete the deal.
The teams later confirmed the trade.
The Rams initiated the trade, a source told Breer and NFL.com and NFL Network's Steve Wyche. Their pursuit of Hunter was influenced by offensive coordinator Brian Schottenheimer, who coached the tackle for five seasons in New York. Shottenheimer used Hunter as a jumbo tight end and swing tackle and believes he'd do well with a fresh start.
Smith's role for the Jets will be the same as Hunter's was -- as a reserve swing tackle and backup tight end, a source with knowledge of the Jets' thinking told Breer. Austin Howard, who took Hunter's job as starter last week, will remain the Jets' starter at right tackle.
The clubs felt a new setting would do both players well.
Smith was the No. 2 overall draft pick out in the 2009 NFL Draft, but the Baylor All-American never lived up to his potential with the Rams. He was envisioned to be the team's left tackle for a decade, but concussion issues and subpar play on the right side defined his three seasons. He recently lost his starting job to Barry Richardson.
This marks the second time this summer the Jets roll the dice on a disappointing former first-round draft pick. The team acquired right tackle Jeff Otah from the Carolina Panthers in July, but the trade was voided when Otah couldn't pass a physical.
It was an encouraging performance for Howard, but the Jets still felt the need to improve the weakest link on their line.
Smith -- who took a huge pay cut this spring -- is guaranteed $4 million this season, $1.55 million more than Hunter. Smith is due a whopping $12 million next season, but ATL's Bryan McIntyre reports that contract voids five days before the start of the 2013 league year if he plays 31 percent of his team's snaps.
Smith was a huge disappointment for the Rams, and the Jets' willingness to bring him shows just how vulnerable they feel at right tackle. Wayne Hunter, meanwhile, likely feels like a kid on Christmas.
Follow Dan Hanzus on Twitter @danhanzus.