Omitted from the Scotland squad for the Euros and limited to mostly brief substitute appearances in the last few months of the season, there were question marks over his time at Parkhead, with both Aberdeen and Hibs monitoring the 30-year-old’s situation.
However, the former Wolves forward has signed on for at least another 12 months with the Hoops and is keen to add to his 123 goals in 261 games.
Speaking to the club’s official website Griffiths said: "I am delighted to extend my time at the club. Celtic is a club I love and want to do all I can to play my part again in bringing success to our supporters.
"I'm looking forward to the season ahead and working with the new gaffer and the rest of the lads. It is an exciting time for the club and I wanted to be part of the club’s future. I'll be doing everything I can to help us get back to where we all want to be."
Manager Ange Postecoglou added: “I am really pleased to keep Leigh with us for another season at least. I have had very positive conversations with Leigh and he clearly understands my expectations and more importantly the club’s.
"Leigh has already proven himself as one of the top strikers in Scotland and I look forward to working with him so that we can bring success to Celtic."