The move capped a week of changes on Cleveland's coaching staff after the team went 0-16.
Earlier this week, the team parted ways with David Lee (quarterbacks), Shawn Mennenga (special teams assistant), Stan Watson (special teams quality control) and Kirby Wilson (running backs/run game coordinator).
"At the end of each season, you have to evaluate everything," Jackson said in a statement released by the team. "The coaching staff is obviously a big part of that process and it starts with me. The truth of the matter is, we need to improve in every area. These are difficult decisions and for the coaches we've decided to part with, we thank them. They are good men, that have worked extremely hard and I appreciate their efforts.
"Adam Henry and Ken Zampese are two really good coaches that I was fortunate to work with earlier in my career. They have successful track records, having coached and helped develop some really good football players. They will demand a lot of our players and challenge them to become their best."
Zampese is the third different quarterbacks coach in Hue Jackson's tenure.
Pep Hamilton served in that role when the Browns ranked last in the league in passing touchdowns while going 1-15 in 2016. Lee oversaw DeShone Kizer, who threw for 11 touchdowns and 22 interceptions in his rookie season while the Browns ranked 28th in passing TDs and became the second team to go 0-16.
Zampese will likely be responsible for the development of USC quarterback Sam Darnold or UCLA quarterback Josh Rosen. The Browns are expected to use the top overall pick on Darnold or Rosen.
Zampese, 50, was fired from his role as the offensive coordinator two games into the season by Cincinnati Bengals coach Marvin Lewis after the team did not score a touchdown. He was the Bengals quarterbacks coach from 2003 to 2015 before being elevated to offensive coordinator in 2016.
Jackson and Zampese also worked together in Cincinnati for three seasons (2004-2006) when Jackson was the receivers coach.
He also has worked as an assistant coach with the Philadelphia Eagles (1998), Green Bay Packers (1999) and St. Louis Rams (2000-2002). With the Rams, Zampese was part of a team whose offense set a league record by scoring at least 500 points in three straight seasons.
His father, Ernie Zampese, was an assistant coach for 36 years and is known for engineering the "Air Coryell" offense with the San Diego Chargers in the late 1970s and early 1980s with quarterback Dan Fouts.
Henry comes to Cleveland after spending the previous two seasons as the wide receivers coach with the New York Giants, who lost Odell Beckham Jr. to a season-ending leg injury in Week 5. In 2016, Beckham's 101 receptions were the second-highest in Giants' history.
Henry also spent one season in the same capacity with the San Francisco 49ers while working with veteran Anquan Boldin, who totaled 69 catches for 789 yards.
Henry also spent five seasons as an assistant coach with the Oakland Raiders from 2007 to 2011, where he worked with Jackson for two seasons. As tight ends coach from 2009 to 2011, he helped develop Zach Miller, who became the first tight end in Raiders' history to lead the team in receiving in three straight seasons.
In between his tenure in Oakland and his most recent stops with San Francisco and New York, Henry also worked with Beckham and Jarvis Landry as the receivers coach at LSU from 2012-14.