Paul will take up the new position from Jan. 3. She is currently the CFO and vice president of Amazon Studios, the film and web series producing unit of Amazon.
The transition comes at a time when Lyft and rival Uber are attempting to cut costs to make up for a decline in ridership and a lack of drivers due to the pandemic.
"There will be no spoilers today, but I have found an exciting frontier opportunity with mission-driven founders focused on serving their community," Roberts said in a LinkedIn post.
Lyft said Roberts' departure is not the result of any dispute or disagreement with the company or its board.
"Over the past seven years, Brian has made a huge contribution to Lyft. With his support and leadership, Lyft went public and reached adjusted EBITDA (earnings before interest, taxes, depreciation and amortization) profitability -- two critical milestones," said Logan Green, Lyft's co-founder and chief executive officer.
Before joining Amazon, Paul, 54, served as the CFO of Hulu for six years, prior to which she worked at Walt Disney Co for 19 years in senior finance, strategy and business development roles.
Roberts will remain as an adviser until June 2022 to assist with the transition, Lyft said.
(Reporting by Manojna Maddipatla in Bengaluru; Editing by Amy Caren Daniel)