According to the network, he directed further questions about his future role to the Trump campaign.
"We love Brian," Tricia McLaughlin, Mr Ramaswamy’s communications director, told CBS. "It’s a good move for Brian and we’re happy for him."
According to The Messenger, which first reported the news, more details will be released about Mr Swensen’s new role soon. He is due to begin on Friday, a source told the outlet.
Mr Swensen is reportedly a close ally of Susie Wiles, a senior Trump adviser, having worked with her on previous campaigns including Ron DeSantis’ gubernatorial race in 2018 and Mr Trump’s reelection campaign in 2020.
News of his departure comes less than 50 days from the Iowa caucuses on 15 January 2024.
Many have viewed the move by Mr Swensen as further sign of Mr Ramaswamy’s dwindling momentum, after making a splash earlier this summer.
Earlier this month, the Ramaswamy team’s videographer, Brandon Goodyear, also stepped away from the campaign, a source familiar with the departure told CNN.
Mr Trump still leads the Republican field by a considerable margin, with national polling site FiveThirtyEight putting him at 60 per cent.
Mr Ramaswamy currently sits in fourth place, with 5.1 per cent, behind Ron DeSantis and Nikki Haley.
Yet he has remained confident, telling reporters in Iowa earlier this month: "We’re sitting exactly where I want to be and I’m confident that we have the momentum ahead of us to be the nominee and more importantly to win this election in a landslide.”