Some 55 per cent of people under 35 said the referendum has made them more likely to vote, with 38 per cent saying they are much more likely, a TNS poll of 933 people over 16 found.
The “referendum effect” has made everyone more politically engaged, with 37 per cent across all age groups now more likely to vote, it found.
Nearly a third (32 per cent) are now more likely to get involved in public debates about local or national issues, rising to two-fifths (40 per cent) among those aged 16 to 34.
The Scottish National Party is the most widely trusted to deliver new powers for Scotland at 37 per cent, rising to 43 per cent amongst those aged 16 to 34.
Just 15 per cent trust Labour, 8 per cent trust the Conservatives and 1 per cent trust the Liberal Democrats to deliver more powers, while a quarter said they do not trust any party.
Those in the younger age group (16-34) were more likely to trust the SNP (43 per cent) and less likely to trust no party (20 per cent). Half (51 per cent) of those who said they were more likely to vote in future elections said they trusted the SNP.
Nearly a quarter (24 per cent) said they trust SNP leader-in-waiting Nicola Sturgeon most to deliver more powers, double the figure for outgoing leader Alex Salmond.
Just 6 per cent trust David Cameron to deliver on his vow of more powers, while 1 per cent trust Ed Miliband and only a handful named Nick Clegg.
In spite of not being a party leader, Gordon Brown (15 per cent) is the UK politician most trusted to deliver more powers, while a quarter (26 per cent) said they did not trust any of those named.
Tom Costley, head of TNS Scotland, said: “This is our first indication of the referendum effect - whether the remarkable turnout in that vote, and the high level of public engagement in the campaign, will carry on into future political campaigns and elections.
“The indication from the poll is that many people, and young people in particular, are energised to continue to take a more active part in political life.
“But the poll also shows that all of the main political parties, especially the unionist ones, have a lot of work to do to convince voters in Scotland that the promise of further devolution will be fulfilled.”
Asked how they had been engaged during the campaign, 62 per cent said they had taken part in discussions with friends and family, 60 per cent watched the TV debates, 11 per cent had contributed to online discussions, 9 per cent had attended a public meeting and 5 per cent had worked for one of the campaigns.