The music legend made the declaration as the Let's Stay Together campaign sought support on the streets of Liverpool today, organisers said.
Sir Paul added his name to an open letter to voters which says: "The decision on whether to leave our shared country is, of course, absolutely yours alone.
"Nevertheless, that decision will have a huge effect on all of us in the rest of the United Kingdom.
"We want to let you know how very much we value our bonds of citizenship with you, and to express our hope that you will vote to renew them.
"What unites us is much greater than what divides us. Let's stay together."
Let's Stay Together say more than 50,000 people have put their names to the letter ahead of next month's referendum, with several hundred celebrities and public figures giving their public support.
Sir Mick Jagger, Sir Bruce Forsyth, Dame Judi Dench, Simon Cowell and Professor Stephen Hawking are also among the signatories.
England World Cup winner Sir Bobby Charlton joined them yesterday, said the campaign.
TV historian Dan Snow, one of the campaign co-ordinators for Let's Stay Together, said: "Sir Paul is one of Britain and the world's most respected musicians. We are humbled that he has signed the letter.
"Sir Paul's signature, alongside Sir Mick Jagger's and those of tens of thousands of people from all over the country, shows that English, Welsh and Northern Irish people hope passionately that the Scottish vote to renew their bonds of citizenship with us.
"The decision is for the Scottish voters alone. Let's Stay Together simply want them to know that we hope that they will stay part of our shared country."
Mr Snow was joined by former Everton footballer Peter Reid in the city centre as they urged locals to put their names to the open letter.
Ex-Liverpool footballer Ian Rush has also added his signature and appeared in the campaign's launch video. Let's Stay Together has toured across England with cities visited including Birmingham, Southampton, Cardiff, Leeds and Manchester.
Scottish Labour MP Anne McGuire said: "We are glad to have the Help! of Sir Paul McCartney. It is hardly surprising that Sir Paul wants us to Come Together. Maybe rather than trying to take us all on a Magical Mystery Tour Alex Salmond should just Let it Be."
A spokesman for Yes Scotland said: "It's fantastic that Sir Paul loves Scotland, and we're sure he will continue to do so after Scots say 'Yeah, yeah, yeah'.
The case for Yes is a democratic one - as far as Scotland is concerned the Westminster system belongs to Yesterday, and independence will be good for the Mull of Kintyre and all of Scotland. Yes is definitely the best Ticket To Ride."