The referendum on Sunday was supported by between 74 and 77% of voters; between 19 and 21% voted "no", the television said. Turnout was between 45 and 47%.
The vote is seen as a crucial test for Jose Luis Rodriguez Zapatero, the Spanish prime minister, as he seeks to rally support for peace talks with Basque separatists.
The exit poll was broadcast shortly after voting ended at 8pm (1800 GMT).
The vote would give Catalonia, home to Spain's second city Barcelona, more power and a greater slice of its income tax and more spending.
A "yes" vote is also seen as a victory for the Zapatero government, which is inclined to give more autonomy to Spain's already powerful regions.
Catalonia statute has been the subject of bitter dispute between regional and national political parties for more than a year, centring on a phrase that says Catalonia perceives itself as "a nation".
Compromise on that phrase in the final statute was eventually rejected by both ends of the political spectrum - the right-leaning Popular Party (PP), which says it is a threat to Spanish unity, and the Catalan nationalist party Esquerra Republicana (ERC), which says it does not go far enough.
The PP has accused the prime minister of selling out in both Catalonia and in the Basque country, where the government aims to start peace talks with ETA separatists after they declared a cease-fire in March.