The Conservative former prime minister said data showed the UK's recovery has begun, with employment and the stock market rising.
He also urged Tory MPs to rally behind David Cameron amid mutterings about his leadership, and predicted a two-tier Europe.
Speaking on the 20th anniversary of Black Wednesday, which marked Britain's dramatic exit from the exchange rate mechanism, Sir John said the UK's economic recovery was under way, despite gloom surrounding the eurozone.
He likened today's UK economy to the early 1990s when Chancellor Norman Lamont was mocked for claiming he could see the "green shoots of economic spring".
The ex-prime minister said: "Norman Lamont was taken to pieces by commentators for suggesting there were green shoots, but in retrospect we can see that Norman was right.
"Recovery begins from the darkest moment. I'm not certain, but I think we have passed the darkest moment," Sir John told BBC1's Andrew Marr Show.
He added: "Why in the depths of this recession is employment growing? Why is industrial production going up? Why has the stock market risen? My guess – and this is something a minister can't say but I can – is that in due course we will find that [we have] passed the bottom."
Sir John also said the eurozone crisis was pushing the 17 countries in the currency union closer together. He said the process could take up to 10 years and would spark a UK referendum on the EU.
He backed Mr Cameron to lead the Conservatives into 2015 General Election, dismissing claims London Mayor Boris Johnson could oust the Tory leader.