The Scottish FA says the paperwork for the player who joined Celtic from Ashdod in 2012 was completed in time before the 23:00 GMT deadline.
But their English counterparts have different rules regarding work permits.
And the 28-year-old, who has played 51 times for his country, does not automatically meet the FA's criteria.
Because Nigeria are ranked 50th in the world, he would require to have played at least 75% of their country's matches over the previous two years.
Ambrose played twice last year and three times in the previous 12 months.
The defender has fallen out of favour at Celtic this season since Brendan Rodgers took over as manager.
He has only made two appearances, the last being a Champions League qualifier against Astana in July.
Should he join Blackburn, he could partner former Celtic team-mate Charlie Mulgrew, who made the switch last summer, in the Championship side's central defence.
However, he has also played at right-back and for Nigeria in central midfield.
His move came on a day when Chelsea failed in a bid to sign Celtic goalkeeper Craig Gordon, while nothing came of reports of interest from the English Premier League leaders in his team-mate, striker Moussa Dembele.
The only other movement out of Celtic on deadline day was goalkeeper Leo Fasan and defender Jamie McCart joining Port Vale and Inverness Caledonian Thistle respectively on loan and winger Michael Duffy leaving on a permanent transfer to Irish club Dundalk.

A tentative deal is believed to have been reached in talks with senior US Justice Department officials.
The fine relates to the sale of securities based on home loans, which led to the near-collapse of the banking system in 2007.
If confirmed, it would be the biggest settlement ever paid by an US company.
Last month, JP Morgan was fined almost $1bn in the "London Whale" scandal, which arose from huge disastrous bets on the financial markets placed by former bank employee Bruno Iksil.
The tentative deal to pay the $13bn fine to the Justice Department was reached during the talks on Friday, between JP Morgan lawyers with US Attorney General Eric Holder and his deputy Tony West, the Wall Street Journal said, citing officials familiar with the decision.
The New York Times also reported that the investment bank was nearing the agreement. Neither the Justice Department nor the bank was available for comment.
But the reports said that while the fine would settle all civil claims, the US bank would still face possible federal criminal charges being pursued in California or individual criminal claims.
The $13bn sum is said to include $9bn in fines and a further $4bn in relief for struggling homeowners.
In the run-up to the financial crisis, sophisticated financial products known as mortgage-backed securities were created by many investment banks.
These special bonds contained a mix of investments but at their heart were supposed to be risk-free home loans, the BBC's business correspondent Joe Lynam reports.
When the housing bubble burst, the value of these assets fell sharply and the credit markets seized up. The balance sheets of many US and European banks, including those in the UK, became toxic and they had to be bailed out by their governments.
What JP Morgan is alleged to have done was sell the mortgage-backed assets knowing full well that many of the home loans were in fact very risky.
Some of the problems relate to mortgage bank Washington Mutual and investment bank Bear Stearns, two failing firms that JPMorgan took over in 2008.
The mortgage-backed assets played a central role in the near collapse of the banking system when banks realised in 2007 that many of their assets were worth a fraction of their official book value.
JP Morgan had initially aimed to persuade Justice Department officials to drop the criminal investigation but the attorney general ruled that out, reports said.
The bank is not alone in facing inquiries into past practice. In August, US government officials filed two lawsuits against Bank of America relating to mortgage-backed securities. Bank of America denied civil fraud in failing to disclose risks and misleading investors.
JP Morgan has found itself overwhelmed by mounting legal troubles lately.
Once the darling of Washington and Wall Street, it reported a rare quarterly earnings loss last week, mostly due to legal costs totalling $9.2bn.
The bank lost $380m during the quarter, compared with a profit of $5.7bn in the same period last year.
JP Morgan says it has set aside a fund of $23bn to deal with mounting legal costs.
Efe Ambrose's proposed loan move from Celtic to Blackburn Rovers is awaiting an English FA ruling over a work permit for the Nigeria defender.
[NEXT_CONCEPT]
US banking giant JP Morgan is set for a record $13bn (£8bn) fine to settle investigations into its mortgage-backed securities, US media reports have said.