The 30-year-old has been a mainstay of the side since arriving in January 2012 from Rosenborg and Brendan Rodgers was keen to have the player signed up as his deal drew to a close.
He said: “I’ve been here for a long time and I really enjoy my life here and playing for Celtic.
“We have a chance to take the treble now and we’ve obviously not done that yet, but everyone wants to just continue to develop as a team, continue to play against good sides and learn.”
Having spent five years already at Celtic, the player found it difficult to pick a highlight of his time so far, but the games against Europe’s elite inevitably come to mind.
Lustig added: “There have been plenty of things. To win five titles in a row, and going for six, has been brilliant.