Goals by Gary Hooper and Georgios Samaras had the game tied up by the interval but an emphatic Light Blues victory at Kilmarnock made it academic.
Celtic substitutes Shaun Maloney and Paddy McCourt grabbed further goals to secure an easy victory but it was not enough to prevent the Hoops finishing second to Rangers for the third successive season.
The home side dominated the opening stages, but failed to open the scoring with Scott Brown and Samaras missing good chances.
But on the half-hour mark Celtic's pressure paid off when Hooper finally put them ahead. When right-back Mark Wilson's cross came in to the packed Well box, Hooper got the break of the ball before poking it past Lee Hollis from eight yards.
Celtic turned the screw further and Hollis made another save in the 36th minute, this time from Sung-Yeung Ki's angled drive, before making another block from the same player moments later.
But in the 40th minute the Fir Park keeper was helpless again when Samaras had the easy task to slide the ball in from 12 yards after being set up by Charlie Mulgrew.
It was more of the same after the interval as Celtic continued to dominate. They grabbed a third in the 53rd minute when Maloney drove past Hollis from 12 yards after creating space for himself.
In the 66th minute, as the tempo dropped further, Jonathan Page came on for Shaun Hutchinson while McCourt replaced James Forrest and five minutes later, the former Derry City player drove past Hollis to make it four.
The hosts' effort proved in vain, though, as they missed out on the league title by a point.
Source: PA
Source: PA