The person spoke to The Associated Press on condition of anonymity because the deal hadn't been announced by the team. It was first reported by Yahoo Sports.
His agent, David Mondress, did not immediately respond to messages left by the AP seeking comment.
Ezeli, a 6-foot-11 native of Nigeria, was drafted with the 30th pick in the 2012 draft by the Golden State Warriors. Last season he averaged 7.0 points and 5.6 rebounds in 64 games, including 13 starts.
Ezeli missed 31 games this season after having arthroscopic surgery in February to remove debris from his left knee.
After starting 41 games for the Warriors his rookie year, he missed the entire 2013-14 season after surgery to reinforce the ligaments in his right knee.
Napier was selected by the Charlotte Bobcats with the No. 24 overall pick in the 2014 draft out of Connecticut. He was traded to Orlando a year ago, and averaged 3.7 points and 1.8 assists in 55 games last season.
"Shabazz is a talented young player that we are pleased to add to our program. He fits the model we instituted last year and we look forward to helping him grow as a player in our system," said Neil Olshey, Portland's president of basketball operations.
Layman was selected with the 47th overall pick in this year's draft by Orlando before he was traded to the Blazers. He averaged 10.2 points and 4.8 rebounds in four years at Maryland.
Portland and Turner agreed on a four-year, $70 million contract at the start of the NBA's free agency period.
Turner, who was drafted No. 2 overall by the 76ers in 2010 out of Ohio State, spent the last two seasons with the Boston Celtics. The 6-foot-7 wing averaged 10.5 points, 4.9 rebounds and 4.4 assists as Boston's sixth man last season, his best since 2013-14.
Turner spent his first three seasons in Philadelphia before one with the Pacers. He's averaged 10.7 points, 3.8 assists and 4.9 rebounds per game over his career.
"He is a really good, alert defender, both on and off the ball," coach Terry Stotts said. "He fits into our culture in how we want to play, both on and off the ball."
Turner told reporters he had admired former Blazer Brandon Roy.
"I was a big B-Roy fan back in the day in college," Turner said. "If it worked for him, it'll work for me."
Portland was one of the biggest surprises of last season, advancing to the second round of the playoffs with one of the youngest rosters in the league after losing four starters in the offseason.
AP Basketball Writer Jon Krawczynski contributed to this report.