"I had a chance to meet with Alex Smith this week and we had a very honest and real discussion," Rivera said in a statement.
"We had a chance to reflect on the 2020 season and talk about moving forward into next year. After the conclusion of that meeting, we decided that it would be best for both parties to move on, and we will be granting Alex his request to be released.
"I want to thank Alex for his contributions this past year. He made such an impact on our young roster, and his leadership was one of the key factors in our late season success ... Everyone here in Washington wishes Alex and his family the best going forward and appreciate all that he gave to our organization."
Smith helped Washington capture the NFC East crown in 2020 after spending two years recovering from 17 leg surgeries. The veteran signal-caller's efforts netted him the Comeback Player of the Year award.
Reports surfaced last week that the two sides were expected to part ways. The 36-year-old had no guarantees left on his contract, and the club was expected to prioritize its young players moving forward.