Meram, who is coming off a career year for the Crew, will fetch Columbus $750,000 in targeted allocation money (TAM) and $300,000 in general allocation money (GAM). The Crew will also receive a 2019 international player slot from Orlando City.
The trade was first reported by ESPN FC.
The 29-year-old Meram set a career high in goals this season, scoring 13 times in 34 games for the Crew. He added seven assists, which was the second-best mark of his career following 13 assists in 2016.
The Michigan-born Meram, who represents Iraq internationally, was reported to have requested a trade from the Crew this winter.
"An emotional day for myself as I say goodbye to the club who drafted me, molded me into the person I am today and gave me the opportunity to fulfill my dream as a professional for seven years," he wrote on Instagram.
"The fans have welcomed a Michigan man into Ohio as one of their own. My coaches have helped me raise my level on the field, and my teammates who I battled with every day at training and under the lights! Thank you Columbus. This was not easy for me by any means asking to move on but it was time. Time for me to be fearless and move on to the next chapter of my life with new challenges.
"Orlando City SC... I am so excited for this opportunity, your belief in me and I am ready to help this club achieve great things in the near future."
Both Columbus and Orlando have seen significant overhauls this winter. The Crew dealt striker Ola Kamara to the LA Galaxy earlier in January in a deal that netted Columbus United States international Gyasi Zardes and $400,000 in allocation money.
Orlando City, which saw legend Kaka depart at the end of the season, acquired playmaker Sacha Kljestan from the New York Red Bulls in early January, trading away Carlos Rivas and Tommy Redding in the deal.
The Lions also added 19-year-old attacking attacking midfielder Josue Colman as a young designated player from Club Cerro Porteno of Paraguay's Primera División. They also traded for the rights to highly-rated college midfielder Cam Lindley, acquiring the North Carolina standout from the Chicago Fire for Rafael Ramos.
Selected by the Crew with the 15th pick in the 2011 MLS SuperDraft, Meram has played in 188 regular-season games for the Crew, scoring 37 goals and adding 33 assists over that span.
Meram was a member of the Crew side that fell in the 2015 MLS Cup final to the Portland Timbers. He signed a new contract with the Crew prior to the 2017 season.