The agency pitched for the account in March. The work was previously handled by Biglight.
Recently iProspect won Specsavers' international digital strategy account, while Manning Gottlieb OMD handles the brand's media planning and buying. Above-the-line advertising is created in-house by Specsavers.
In January, Specsavers brought back the Basil Fawlty character, played by John Cleese, from the classic comedy Fawlty Towers.
Richard Holmes, the group marketing director at Specsavers, said: "Possible’s knowledge of the digital space and the passion they showed for the brand and our business was evident throughout the process.
"They really demonstrated their understanding of who we are, what we stand for, and the best way to translate that into an authentic online and mobile experience."