American Andretti, the 1991 CART champion and son of 1978 Formula 1 world champion Mario, had been seen as the clear frontrunner from as many as seven initial expressions of interest.
Andretti Global announced in January a partnership with General Motors' Cadillac brand for a US-owned team with at least one American driver.
The International Automobile Federation (FIA) said in a statement that Andretti Formula Racing LLC was the only applicant sent forward for commercial discussions with Formula 1 from the four that made the second stage of the process.
Liberty Media-owned Formula 1 noted the FIA's conclusions and said they "will now conduct our own assessment of the merits of the remaining application".
Final approval is not a given, with Formula 1 chief executive Stefano Domenicali sounding reluctant in the past to expand the grid and saying any decision had to be right for the business.
The FIA started the formal application process in February, seeking to identify one or more new teams interested in joining in 2025, 2026 or 2027.
"The FIA is obliged to approve applications that comply with the Expressions of Interests application requirements and we have adhered to that procedure in deciding that Andretti Formula Racing LLC's application would proceed to the next stage of the application process," said FIA president Mohammed Ben Sulayem.
"In taking that decision, the FIA is acting in accordance with EU directives on motorsport participation and development," he added.
"Andretti Formula Racing LLC was the only entity which fulfils the selection criteria that was set in all material respects. I congratulate Michael Andretti and his team on a thorough submission."
Alpine has said it would supply engines if Andretti secures a slot but the Renault-owned outfit has since replaced the team bosses involved in that decision.
General Motors' involvement may also come under closer scrutiny with the big three Detroit car makers hit by United Auto Workers (UAW) union strikes as they seek cost reductions to help accelerate a shift to electric vehicles.
The FIA statement made clear the approval was for Andretti, mentioning General Motors only in relation to interest in the new power unit regulations for 2026.
Honda and Audi will be entering then, the former with Aston Martin and the latter after taking over Swiss-based Sauber, expanding the pool of possible engine options to six from a current list of four.
The FIA statement did not say which year Andretti were looking to debut.
That timing may be complicated by the current 'Concorde Agreement' - the three-way deal between the commercial rights holder, teams and FIA - expiring at the end of 2025 and needing to be re-negotiated.
The current 10 Formula 1 teams have been lukewarm towards expanding the grid, wary of diluting the overall pot of revenues.
Some also feel the current $200 million (£165 million) entry fee, which would be shared among the existing 10 teams as compensation, is not enough.
The FIA said its assessment of applicants included criteria such as sustainability and societal impact, in line with the sport's target of being net zero by 2030.
Failed applications included New Zealand-based Rodin Cars, who had committed to reserving one seat for a female driver, and a Hitech team backed by Kazakh billionaire businessman Vladimir Kim.
fee, which would be shared among the existing 10 teams as compensation, is not enough.
