"To sign a new contract with Liverpool is unbelievable for me," Suarez told the club website.
"I am happy off the pitch because the people of Liverpool are good with me and my family. I try my best on the pitch and when you are happy off the pitch, you are happy on the pitch."
"The fans... are our 12th player. The supporters of Liverpool are unbelievable."
Suarez met with new manager Brendan Rogers for the first time on Monday as he returned to the club after playing for Uruguay at the Olympic Games.
Media speculation had linked him with a possible move to Juventus, but he was quick to extend his future at Anfield.
The 25-year-old's initial contract, signed following his reported £22.8 million move from Ajax in January 2011, was due to expire in 2016.
In one-and-a-half seasons at Liverpool, Suarez has made 52 appearances and scored 21 goals.
During the 2011/12 season he scored a memorable hat-trick against Norwich City that included an audacious lob over the goalkeeper from 45 metres.
Suarez also served an eight-match ban and was fined £40,000 pounds after he was found guilty of racially abusing Manchester United's Patrice Evra.
He fuelled further aggravation when he failed to shake the Frenchman's hand during a second meeting at Old Trafford in February, for which he later apologised.
He has been a key figure in Uruguay's recent revival, helping them reach the World Cup semi-finals in 2010 and win the Copa America the following year.
