Vancouver also receives an international roster spot in 2018.
Parker is entering the final year of his contract and requested a trade earlier this offseason, according to a report from MLSsoccer.com. The 25-year-old reportedly asked for a contract that would pay him $1.8 million over three years and requested to be dealt after Vancouver countered with $1.4 million over three years.
Parker made just $99,600 last season in Vancouver, where he was second in MLS with 86 headed clearances and fifth with 73 aerials won in 32 starts in 2017. He is a native of Hicksville, N.Y.
"Tim is the type of defender we look for," Red Bulls head coach Jesse Marsch said in a team release. "His soccer knowledge, athleticism, and one-on-one defending ability are qualities that fit with what we ask of our center backs. I know he is glad to be coming home to New York, and we think he will thrive in our style of play."
Felipe, 27, had two goals and five assists last season. He scored 10 goals and had 17 assists in 100 games, all starts, with New York over three years and agreed to a new contract with the Red Bulls last summer that reportedly will pay him just under $450,000 over the next two seasons.
"Felipe has consistently proven to be one of the best box-to-box midfielders in Major League Soccer," Whitecaps head coach Carl Robinson said in a statement. "He's fiercely competitive, very comfortable on the ball, and creative going forward. We firmly believe he's someone that will make the players around him better and we're delighted to add him to our group in the prime of his career.
"As always, this decision was made in the best interest of our club in the short, medium, and long term. We are thankful to Tim for his contributions over the last three seasons and wish him well moving forward."
Vancouver kicks off its season Sunday against the visiting Montreal Impact. The Red Bulls open March 10 with a home game against the Portland Timbers.
--Field Level Media