The legislation fulfils a main promise in a peace accord struck last year with Free Aceh fighters in the tsunami-hit province.
But some former fighters said the law reduced the level of self-rule promised by the government and said they would complain to members of the EU monitoring mission deployed in the province.
The law gives Aceh control over 70% of its mineral wealth and allows former rebels to run in elections expected this year.
Munawarliza Zain, a spokesman for the former fighters, criticised several sections of the bill, saying it gave too much authority to the central government and left the role of the military unclear.
Ferry Mursyidan Baldan, a legislator who headed the committee overseeing the bill, said: "We are very aware that what we have achieved is not perfect, but this is the best we could do."