Griffiths, 28, has been rewarded with a new deal after scoring 100 goals in 190 appearances since joining the club in 2014.
The Scotland international has been an integral part of the side that have now won seven straight titles, and wants to make history by going for 10-in-a-row, one more than the record shared by Celtic and Rangers.
"I'm here for 10 so that's a start," Griffiths told Celtic TV.
"My main focus now is trying to get back in the team and stay as fit as possible, and try and get my goal tally up. I've hit the 100 now and I want to try and continue that and aim for more heights."
Griffiths has had to battle with Moussa Dembele, who moved to Lyon last month, and Odsonne Edouard for his place since Celtic boss Brendan Rodgers's arrival in Glasgow.
But he remains a fans' favourite and is glad to have finally concluded prolonged talks over an extended contract.
"I'm over the moon. It's been a long time coming, talks have been ongoing for a while now and I'm so glad to get it over the line.
"The main aim is to be here for as long as I can, and for Celtic to have shown that faith in me to sign me for another four years makes me ecstatic."