The couple said they were "committed to continuing" a content deal worth an estimated $25m (£18m) and will continue to lobby Spotify bosses for changes.
Top artists have pulled songs from the streaming service in protest at its work with Joe Rogan, a US podcast host who has interviewed vaccine-sceptics.
Neil Young is among those to cut ties.
In a statement, a spokesperson for the Sussexes' Archewell Foundation warned of the impact of "rampant mis and disinformation".
They added: "Last April, our co-founders began expressing concerns to our partners at Spotify about the all too real consequences of Covid-19 misinformation on its platform.
"We have continued to express our concerns to Spotify to ensure changes to its platform are made to help address this public health crisis.
"We look to Spotify to meet this moment and are committed to continuing our work together as it does."
Archewell Audio, the California-based Sussexes' audio production company, lists just one podcast on Spotify, a "holiday special" published in December 2020.