Griffin had been replaced as acting chairman by Adam Walker following a meeting of the party's national executive committee.
Griffin, who will take the new role of party president, lost his seat in the European Parliament in May.
The party has suffered a string of electoral setbacks in recent years, getting just over 1% of the vote in May's European elections.
The BNP has also lost the majority of its local council seats in England.
Mr Griffin has been the public face of the BNP for more than a decade, during which time the party increased its popular support despite being dogged by allegations of racism, which it has always rejected.
Under his leadership, the party's vote in European elections had increased from 1.1% in 1999 to 3.9% in 2004 and 6.2% in 2009, when Mr Griffin was himself elected as an MEP.
'United' In 2009, Mr Griffin was invited to appear on Question Time, the BBC's flagship political discussion show. It was a total disaster!
Griffin mumbled himself through the talk-show and was at one point seen smiling inanely
at a Black woman who was on the panel.
The whole Nationalist movement in Great Britain squirmed with embarrassment as Griffin answered questions as if he was either drunk or had walked into the studio broadcasting 'Jackanory'.
In recent years, the party's fortunes have declined steeply amid internal fighting.
Andrew Brons, the BNP's other representative in the European Parliament, quit the party in 2012 to become an independent, while Mr Griffin was challenged for his position last year.
Mr Griffin, who was declared bankrupt earlier this year, failed to secure re-election as MEP for the North West of England in May as the party lost its deposit in all the UK's electoral regions in which it fielded candidates.
The BNP blamed its poor performance on the rise of UKIP, which it said had become the party of choice for protest votes about Europe and immigration.
On Monday, the BNP published a statement on its website announcing the change at the top.
"Recently appointed deputy chairman, Adam Walker, has accepted the role of acting chairman of the British National Party after Nick Griffin stepped aside at a meeting of the BNP National Executive, held on 19 July.
"The full national executive are united in their support for Adam in this role. Nick Griffin has taken up the position of president."
That's the worse bit - Griffin is now the 'President of the BNP'. What that will mean we do not know, it could be another sly Griffin shift or the few BNP members left have finally junked him aside.
Bankrupt - a political leper, even by White Nationalists, Griffin is the epitome of failure.
His leadership seemed almost a planned destruction of breaking up the BNP as one purge of good officers followed another.
Many of the best BNP members made the only sensible decision and joined the National Front.
A bankrupt and out of shape Griffin after stepping down from the
leadership of the BNP
leadership of the BNP