The party's NEC said it had voted by a "clear majority" to exclude Mr Woolfe - previously seen as the frontrunner.
The MEP said he was "extremely disappointed" by the decision, and three NEC members have quit in protest.
Jonathan Arnott, Bill Etheridge, Diane James, Lisa Duffy, Phillip Broughton and Elizabeth Jones are on the ballot.
Speaking to the BBC, Mr Woolfe said he believed the NEC had "their own reasons" for excluding him from the ballot, but implied it could have been linked to the fact he was committed to abolishing the executive.
Asked if he would consider taking legal action, or calling a vote of no confidence in the NEC, Mr Woolfe said it was a matter for the party membership but he thought the contest should continue without him.
Announcing their resignations from the NEC, Victoria Ayling, Raymond Finch and Michael McGough said in a joint statement that the party's governing body "is no longer fit for purpose" and called for a vote of no confidence in the NEC.
They accused it of "deliberately obstructing" Mr Woolfe and some of its members of putting personal ambitions ahead of the interests of the party - which polled more than four million votes at the last general election and got 12% of the vote.
"Steven Woolfe is a popular candidate among UKIP's members and should be permitted to represent those that wish to vote for him," they wrote.
"To purposefully trawl for technicalities upon which to base a decision to deny his inclusion is not in the best interests of the membership and truly injurious to UKIP."
The winner of the leadership contest - sparked by Mr Farage's decision to stand down after the UK voted to leave the EU - is scheduled to be announced on 15 September.
In a statement announcing the final line-up, the party said: "By a clear majority of NEC members Steven Woolfe MEP's application was considered to be ineligible as a result of a late submission and as such he did not meet the eligibility criteria."
Mr Woolfe, the party's immigration spokesman, submitted his nomination papers 17 minutes late on Sunday, blaming the delay on technical issues with the registration site.
He submitted his application at 11:35 BST - before the noon deadline - but it did not successfully go through until 12:17 BST.
He said he had been in contact with party officials prior to the deadline passing to alert them to the problems, and had sent pictures, upon request, to prove it.
The party's chairman, Paul Oakden, said Mr Woolfe's exclusion was "regrettable" but the rules for prospective candidates, as for all elections, were "very clear".
He told BBC Radio 4's World at One that the NEC was put in the position of having "to bend and flex the rules" to accommodate a single candidate and "I think they did not feel comfortable in doing that".
Mr Woolfe said he was "extremely disappointed" not to be on the final ballot as he had wanted to "inject my ideas, plans and passion into the party".
And he criticised the NEC as "not fit for purpose" and said its conduct during the leadership election had "confirmed many member's fears that it is neither effective nor professional in the way it governs the party".
"They have failed to accept that there were serious issues with the application system despite providing evidence that attempts of submission were made before the deadline. The NEC deny this is the fault of the UKIP system.
"Furthermore, highly confidential information about me held in party documents has been leaked to the press and the NEC has not sought to investigate this gross breach of privacy," he added.
Mr McGough - who has resigned from the NEC - said Mr Woolfe's exclusion from the contest was "unfair" and called into the question the party's future.
Unless the party elected a "competent leader who was comfortable with the media, it was finished", he told World at One. "This is a fight for survival. It is life or death."
BBC political correspondent Tom Bateman said the NEC's decision "opens up a whole new schism in UKIP" and he understood that Mr Farage could call an emergency meeting of the party membership to put pressure on the body to reconsider.
Mr Oakden, who only took over as party chairman this week, said the party was perfectly entitled to call an EGM if 25% of its branches backed the move but said talk of a potential split was over-exaggerated and the remaining contenders were a diverse and exciting group.
MEP Ms James - now regarded as the favourite in the contest - has launched her own campaign website while Mr Arnott, an MEP for the north east of England, has said he was won the backing of the party's deputy leader Paul Nuttall.
Of the other candidates, Mr Etheridge is also a member of European Parliament while Lisa Duffy is a councillor in Cambridgeshire. Both Ms Jones and Mr Broughton have stood as candidates in recent parliamentary elections.
UKIP leadership hopeful Steven Woolfe has been ruled "ineligible" to stand in the contest to replace Nigel Farage - after he submitted his papers late.