The vote is of symbolic importance for the future of the treaty
European Commission President Jose Manuel Barroso said he welcomed the result with "great satisfaction".
Prime Minister Jean-Claude Juncker, who said he would resign if there was a "No" vote, said it proved the treaty was not dead.
But the BBC's Caroline Wyatt says it is unclear whether Luxembourg's support is enough to save the charter, which for the time being has been put on hold.
It is unlikely this "Yes" vote from Luxembourg will change that, whatever Mr Juncker may hope, she adds.
'Signs of optimism'
In his first public reaction to the result, Mr Juncker said: "It is the expression of the popular will of a small state but a great nation. This vote was every bit as important as those in France and the Netherlands.
"If Luxembourg had voted 'No', Europe would be in an ultra-serious crisis. With this vote we are still in a crisis but a crisis which lets some signs of optimism appear on the horizon."
Mr Barroso said the vote sent out "a strong signal, because it means that a majority of member states consider that the constitutional treaty responds to their expectations by opening the way for a... stronger Europe on the world stage."
The constitution was rejected by France and the Netherlands earlier this year, and opinion polls in Luxembourg last month suggested a narrow majority in favour.
Unease
Some 230,000 citizens went to the polls in the tiny duchy, one of the European Union's founding members where voting is compulsory.
The vast majority of Luxembourg's politicians, the media and the urban elite were in favour of the treaty and campaigned for a "Yes" vote to prove the constitution could be resurrected.
A survey in June showed that some 16% of voters in Luxembourg were undecided.
French "No" campaigners - mainly from the left - urged Luxembourgers to reject the treaty.
Although Luxembourg is Europe's richest nation and receives more money per head from the EU than any other, there is unease there about the future.
Many worry about cross-border crime, immigration and an unemployment rate which is low but growing.
Results of the referendum, 56.52% '''Jo''' (Yes),  43.48% '''Nee''' (No)

The people of Luxembourg voted a slight yes today on a referendum on the EU Constitution, which was the first national referendum since 1937. A large turnout was expected considering that there is a legal obligation to vote in Luxembourg, overall 220 000 people voted out of 223 000 voters. A close vote was expected as the last opinion poll a month ago indicated a small advantage for the "yes", but a substantial 16% of non-decided.

The results were '''56.52%'''  voted "Jo" (Yes) and '''43.48%''' voted "Nee" (No).

Traditionally, Luxembourgers are pro-European, and all the major parties backed the approval. However globalisation, rising unemployment, immigration & the new Eastern members made some of them feel uneasy, same as in neighbouring France and in the Netherlands where a majority of people rejected the treaty.