With one match remaining, Ajax have 73 points, four more then PSV Eindhoven who stayed on track for a Champions League qualifying berth with a 4-2 win over NEC Nijmegen.
Tilburg were relegated after suffering their 21st defeat.
Iceland's Sigthorsson opened the scoring after 12 minutes with a well-executed diving header following a fine cross from Ryan Babel.
A blunder from Tilburg keeper David Meul, who let a long drive from Eriksen slip through his hands, allowed Ajax to double the lead after 25 minutes.
Viktor Fischer, Siem de Jong and Danny Hoesen scored after the interval as the capacity home crowd of 50,000 celebrated.
"A good result for a championship match though we should have rewarded ourselves earlier as the chances were there already in the first half," said Ajax coach Frank de Boer.
"We deserved this title despite the fact that we dropped points but we showed the most consistency and also played the best football."
After a third straight crown Ajax will now want to focus on winning the Champions League, but fear they could lose players such as De Jong, Eriksen and Toby Alderweireld to foreign clubs.
"This feels great but it would be perfect if this team sticks together for another year so we can try to survive the (Champions League) group stage," said left back Daley Blind, who signed a three-year deal last month.
PSV virtually secured a spot in the Champions League preliminary round when they cruised to victory over NEC Nijmegen to lift their total of goals scored to 102.
The win put them three points clear of Feyenoord who suffered a humiliating 2-0 defeat at ADO Den Haag.
Feyenoord can still pull level on points with Dick Advocaat's team but a far inferior goal difference will make it impossible to leapfrog them.
- Sports & Recreation
- NEC Nijmegen
- PSV Eindhoven
- Danny Hoesen
- Siem de Jong