The 54-year-old Ryan appeared emotionally drained during a 20-minute news conference on Monday.
Lynn, a long-time Ryan assistant, was promoted to coordinator in September, when Ryan fired Greg Roman after an 0-2 start.
Another major decision facing the next head coach is quarterback.
"We mutually agreed that that the time to part ways is now," Pegula said in a statement released by the team. "These decisions are never easy."
This has been a difficult year for the Ryans, who mourned the death of their father, Buddy Ryan, in June.
Ryan replaced Doug Marrone, who opted out of his contract following a 9-7 finish in 2014, and three months after the Pegulas purchased the Bills from the estate of Hall of Fame owner Ralph Wilson.
Ryan had three years remaining on his contract.
Terry Pegula, who made Ryan's hiring his first big splash as owner, was the person who informed Ryan of his dismissal Tuesday. The decision came three days after a 34-31 overtime loss to Miami which eliminated Buffalo (7-8) from contention, and extended the NFL's longest active playoff drought to 17 years.
Assistant head coach and offensive coordinator Anthony Lynn will coach the Bills in their season finale at the New York Jets (4-11) on Sunday,Wholesale China Jerseys. Lynn is also considered a candidate to replace Ryan permanently because of his familiarity with an offense that is closing in on leading the NFL in rushing for a second consecutive season.
Buffalo has allowed 30 or more points five times and allowed more than 400 yards offense four times, both matching last year's total. Opposing running backs also enjoyed three of the top six outings against Buffalo in team history.

Buffalo's drought is tied for the fifth-longest in league history,Cheap Jerseys China, and the longest since the New Orleans Saints failed to make the playoffs during their first 20 NFL seasons (1967-86).
"But if it is,NFL Jerseys From China, it's something I've got to live with," he said.
General manager Doug Whaley's job appears secure after being put in charge of the Bills coaching search, the team's third in four years. Buffalo is also moving on to its eighth coach since the playoff drought began during Wade Phillips' final year as coach in 2000.
Ryan finished with a 15-16 record with Buffalo and is 61-66 overall, including a six-year tenure with the New York Jets. And it was Ryan's hiring by the Bills in January 2015 that electrified a fan base because of his larger-than-life persona and reputation as a defensive specialist.
The Bills also fired Ryan's twin brother, Rob Ryan, from his position as an assistant head coach with the responsibility to oversee defense.
"I'm tired of people talking about the 17 year drought REX was here for 2 of those years hard to build a winner if coach changes every two years," Douzable wrote in a series of posts.
Starter Tyrod Taylor's future is not secure despite signing a lucrative five-year extension and restructuring the final season of his contract in August. The Bills can opt out of the deal after this season.
Bills defensive lineman Leger Douzable voiced his displeasure with Ryan's firing on his Twitter account.
Ryan stirred the fans even more during his inaugural news conference by vowing to build the Bills into a bully.
Miami's Jay Ajayi had 206 yards rushing on Saturday after a 214-yard outing against Buffalo in October. And Le'Veon Bell had 236 yards rushing — the most against Buffalo in franchise history — in Pittsburgh's 27-20 win at Buffalo on Dec. 11.
Pegula then noted his wife in saying: "Kim and I and our entire Bills organization share in the same disappointment and frustration as our fans, but we remain committed to our goal of bringing a championship to western New York."
Last year, the Bills finished 19th in yards allowed — the worst ranking for Ryan in his 11 years as a head coach or coordinator. Buffalo also managed just 21 sacks, a franchise-low for a 16-game season, and after the defense led the NFL with 54 the previous season under coordinator Jim Schwartz.
ORCHARD PARK, N.Y. (AP) — Rex Ryan's inability to back up his boasts of building a bully — particularly on defense — in Buffalo led to the Bills firing their high-profile coach one game short of completing his second full season.
His promises eventually fell short, particularly on defense.
The defense underperformed once again this year,China Jerseys Wholesale, despite Ryan's offseason vows that it'll be improved.
He called the loss to Miami his most painful as a Bills