The new sponsors replace Carling, which became the scheme's first sponsor in May 2005 until last December. The deal was negotiated by CBS Outdoor.
The companies, which are planning new ideas to raise the profile of busking on the Underground, said they will use the deal to target 15- to 35-year-old Londoners who share a "central London" mindset.
The partnership will give thelondonpaper and Capital 95.8 access to 30 co-branded busking pitches on the Tube, multi-format campaigns on CBS Outdoor sites and editorial coverage for both brands across each other's platforms.
Creative for the sponsorship will be created by advertising agency Delaney Lund Knox Warren & Partners.
The agency has created a dedicated website called , where users will be able to access information about the buskers and find out where their favourite buskers are playing.
Nicole Refson, head of marketing at thelondonpaper, said: "Both thelondonpaper and Capital share a very similar outlook on London life - upbeat and positive."
She said the unique tie-up would allow thelondonpaper and Capital 95.8 "to reach each other's audience".
The London Underground busking scheme was originally launched in May 2003 after it won the right in 2001 to change the local bylaws to legalise licensed busking.
Sponsorship helps run the scheme, but the buskers are not paid and rely on the generosity of Tube passengers.
Donna Price, sponsorship manager at CBS Outdoor, said: "This is a highly creative and powerful sponsorship that has brought together two of London's premier media brands to create a campaign that will have massive impact."