The 33-year-old, whose last appearance in the English game were for Wigan Athletic in the Championship, was unveiled at a signing ceremony held at the Komoco Motors Showroom in Jurong.
Pennant had joined Rovers, one of the wealthiest clubs in the country, on a trial basis earlier this month ahead of the start of the season in mid-February.
With a reported salary of £19,500 per month Pennant will be the top earner in the S.League.
On his arrival Pennat said: “I have to thank my teammates for making me feel welcomed since I have arrived.
“They have been fantastic by showing me lots of respect and I have a lot of respect for them too.”
Arsenal broke the record fee for a trainee to sign Pennant for £2 million from Notts County at the age of 15 but he never did enough to earn a place in Arsene Wenger’s side.
Pennat enjoyed his greatest success at Liverpool, where he started in the 2007 Champions League final, and at Stoke.
