But chairman Greg Clarke said the governing body was taking a "leap of faith" in approving the businessman's takeover.
Mr Brent's offer, although strongly backed by fans, was always a last resort for Argyle, and will see creditors – including charities and small businesses – receive less than 1p for every pound they were owed when the club collapsed in March.
In a statement, Mr Clark said: "I would like to welcome James Brent to the Football League and thank him for the efforts he has made to help save Plymouth Argyle Football Club."
But he added: "It is important to place on record that his takeover proposals have required a significant leap of faith by the board, which it has agreed to take in order to preserve the future of professional football in Plymouth.
"In seasons ahead, the League will closely scrutinise the financial affairs of the club to ensure that the promises made to the board are kept."
Mr Brent was at Home Park yesterday afternoon to meet with manager Carl Fletcher and chairman of football operations Peter Ridsdale.
Brent told reporters: "If you look at the financial position of the club compared to other League One and League Two clubs, it is actually remarkably strong.
"A great burden has been lifted from people's shoulders. It's an exciting new beginning."
But any signings the club wants to now make must be individually approved by the Football League.
Mr Clark thanked long suffereing staff who may now see overdue wages paid, and the Argyle supporters and Plymouth City Council, whose £1.6million acquisition of Argyle's stadium was a pivotal part of Mr Brent's rescue.
Whilst it always good to see a club with the traditions of Plymouth survive, the forgotten people in these situations always seems to be the suppliers, large and small that get virtually none of the money owed. The result of this impacts all clubs at the lower levels of the Football League and non-leage football as suppliers restrict credit and extended payment terms to avoid repeat situations. It also threatens to put some of the smaller suppliers out of business.
As a business FTD represents dozens of companies who supply football clubs, and as much as you would hope it won't happen again, bwt there are other clubs in dire straights - one North Western club recently asked staff to take 40% wage cuts in an effort to stay afloat and We fear Plymouth may not be the last.