The Civil Aviation Authority (CAA) has said safety tests showed that jet engines can cope in areas of low density ash.
UK Transport Secretary Lord Adonis announced that all airports could reopen following discussions with the CAA, but he said some restrictions would remain in place.
Among those finally making their way home was Patrick Carrs, 69, from Glasgow, who arrived at Manchester Airport.
He said he and his wife Helen had endured a "horrendous" journey back from Toronto, Canada.
"It was five days in a hotel until we got the plane yesterday," he said.
"We have spent a lot of money we were not expecting to spend.
"We have had no help from anyone and we were left on our own."
Thousands of others remain stranded as a result of the ban, which had been in place for most of the country since Thursday.
A BAA spokesman advised passengers to contact their airline before travelling to an airport as they returned to normal operations.
One of the key lessons of this episode is that we must have the same empirical evidence about conditions in the air as we have on the ground
"Not all flights will operate during the early period of opening, and we will do everything we can to support airlines and get people moving," he said.
Network Rail said engineering work planned for this weekend on the main London to Scotland routes - the East Coast and the West Coast main lines - had been cancelled so more trains could run.
Air traffic control company Nats denied it faced government pressure to ease flight restrictions following the spread of the volcanic ash cloud.
A CAA spokesman said Nats was acting on guidelines that prohibited flights through any type of volcanic ash cloud when it imposed the restrictions last week.
CAA chief executive Andrew Haines said manufacturers had established a threshold of ash concentration above which it was not safe to fly, but below which planes could operate normally.
First Minister Alex Salmond said: "One of the key lessons of this episode is that we must have the same empirical evidence about conditions in the air as we have on the ground upon which to base safe and intelligent decisions, given the extraordinary scale of the economic dislocation and inconvenience we have experienced."
A ferry which normally runs across the Pentland Firth is being used to bring hundreds of people back from Norway to Scotland.
The Northlink vessel was sent from Orkney to Bergen to pick up the passengers and bring them back to Aberdeen.
The BBC spoke to passengers coming off the ferry at Rosyth
Three Thomas Cook aircraft arrived into Glasgow Airport overnight from Heraklion in Greece, Arrecife in Lanzarote, and Sharm el Sheikh in Egypt.
On Tuesday, Scotland's mainland airports had flights to and from the Scottish islands, Iceland, the Faroes, the Isle of Man, Belfast, Durham Tees and Newcastle.
Spare capacity on the Rosyth-Zeebrugge service has been used by passengers stranded on mainland Europe by cancelled flights.
A helpline for passengers stranded due to the volcanic ash cloud and concerned relatives has been launched by the Scottish government.
It is designed to complement the Foreign and Commonwealth Office (FCO) helpline which will remain the main point of contact for travellers needing help while stranded overseas.
The helpline offers "general advice that may be helpful to stranded travellers and their families", including contact details for airlines and travel operators and the latest information issued by travel operators.
The Scottish government helpline number is 0800 027 0504 or from overseas +44 800 027 0504. The Foreign and Commonwealth Office 24-hour consular helpline has been set up on 020 7008 0000 for people stuck abroad.
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As these airports return to normal operations, it is imperative that passengers contact their airline before travelling to the airport
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