The Exiles become the third English Premiership club to hit the wall in eight months after Wasps and Worcester were also suspended over financial difficulties.
London Irish had been given a one-week extension to meet commitments to pay staff and players in full for May and assurances over funding for next season.
In a statement, the RFU said: "As a result of London Irish and its potential buyers being unable to provide reassurances over the club's financial ability to operate in the Premiership in the 2023/24 season, the RFU has confirmed the club is not able to participate in any league next season."
Irish have debts in the region of £30 million and do not own their own stadium, instead playing at Premier League club Brentford's ground.
On Friday they were issued with a winding-up petition by tax authorities.
Coached by former Ireland boss Declan Kidney, the club had finished fifth in the Premiership this season, narrowly missing out on the title-deciding playoffs.
But the future of several rising stars such as England wing Henry Arundell will now lie elsewhere.
"This is desperately sad news for everyone who is part of the London Irish community as well as all the players, fans, staff and volunteers for whom this club means so much," said RFU CEO Bill Sweeney.
"Working alongside Premiership Rugby, the RPA (Rugby Players' Association) and London Irish over recent months, our collective first priority has been to do the utmost to secure the long-term viability of the club and the protection of its players and staff.
"To achieve this, it was imperative that transparent evidence of funding be presented to us...
"Despite requesting this evidence over the last six months and receiving assurances on multiple occasions that we would receive proof of ownership and funds; it has not materialised."
In a statement, Irish said they "remain in active discussions with the RFU as to any circumstances that may result in the suspension being lifted."
The 2022/23 season was heavily disrupted by the collapse of Wasps and Worcester leaving a large number of fixtures unfulfilled.
Sweeney added that avoiding another insolvency midway through next season was part of the rationale to take the decision now.
A hardship fund has been set up by the RFU, Premiership Rugby and the RPA to help players and staff who are most in need of financial support.
