The deal is pending a physical and should be announced at some point this week.
The Red Sox have not confirmed the deal, but general manager Ben Cherington acknowledged that Napoli could soon be joining the team.
"We've made some progress and he's a guy who gets on base, has power and could be a good fit for our ballpark," Cherington said. "We knew when we made the Dodgers trade, and moved [Adrian] Gonzalez, we were going to have to try to find a way to replace that offense and as we got into the offseason, we understood that that was probably going to have to come from a combination of guys and maybe not one guy."
A few days ago, the Sox also acquired outfielder Jonny Gomes. Earlier in the offseason, they got a backup catcher with some pop in David Ross.
"That's part of what we've been trying to do this offseason is add offense at a number of spots on the roster, so we're hopeful we can continue to do that," Cherington said.
Napoli is a powerful pull hitter who is a strong fit for Fenway Park, where he is a .307 hitter with nine homers, 20 RBIs and a 1.138 OPS in 75 at-bats, including postseason.
Though Napoli has been a catcher for most of his career, the Red Sox might make first base his primary position. Napoli has started 118 games at first in his career.
"He could catch, he can play first," Cherington said. "If he's here, we imagine he'd do some of both but that would be up to our manager to figure out."
Boston already has a logjam behind the plate with Jarrod Saltalamacchia, Ross and Ryan Lavarnway.
However, Cherington said it's possible the Red Sox could open the season with all four catchers still in the organization. Lavarnway still has Minor League options.
"Hard to say," said Cherington when asked how much Napoli could catch. "Obviously we're not ready to announce anything. There have been years when he's caught a number of games, a lot, and there's been years he's caught less. We like his offense in Fenway, we like the versatility, so I'm going to say we're hopeful to make some progress there."
The 31-year-old Napoli hit .227 with 24 homers and 56 RBIs for the Rangers in 2012, making his first All-Star team. The Red Sox think Napoli can get back to the level he was at in '11, his first year in Texas, when he hit .320 with 30 homers, 75 RBIs and a 1.046 OPS.
Before his two-year stint in Texas, Napoli spent the first five seasons of his career with the Angels, where he played against the Red Sox in the postseason three years in a row (2007-09).
With this year's free-agent market short on sluggers, Napoli drew significant interest from other teams, particularly the Rangers and Mariners.
Texas didn't want to go longer than two years with Napoli, which was likely the deciding factor in him choosing Boston.
With Napoli soon to be officially on board, the Red Sox can focus on several other needs they have this winter, which include an outfielder, a starting pitcher and possibly a shortstop.
Napoli has played 727 games in the Majors, hitting .259 with 146 homers, 380 RBIs and an .863 OPS.
"Again we don't have anything to announce," Cherington said. "If we were to progress there, we're looking at on-base, power, positional versatility and to collectively replace some of the offense we lost with Gonzalez and improve on the overall lineup performance. Someone like that can help us in a number of those areas."