London-born Williams, 24, has penned a two-year deal with the Tigers, with the club having an option of a further year.
Williams becomes the third capture of the summer for City, who are also being linked with Beverley-born striker Jack Marriott.
McCann said: “We’re delighted to eventually get Randell. We offered a big fee for him this time last year and the boy was very keen to come to us.
“Unfortunately, Exeter weren’t prepared to let him go, so to get him now on a free transfer is quite a coup for us.
“Randell’s got electric pace, loves getting at defenders in one-v-one scenarios, can go both ways and will provide serious competition in the forward areas of the pitch.”
Meanwhile, Doncaster Rovers have moved swiftly to fill the right-back void vacated by Brad Halliday by bringing in Cambridge United’s Kyle Knoyle – their second signing of the close season.
Knoyle enjoyed an outstanding 2020-21 in United’s promotion-winning campaign, with his performances earning recognition from his peers by way of a place in the League Two Team of the Season.
London-born Knoyle, 24, was an ever-present for the U’s, starting each of United’s 46 league games last season and has been described as the best right-back in League Two by head coach Mark Bonner.
But with Knoyle being out of contract at Cambridge at the end of June, he has elected to move on under freedom of contract and join Rovers, which sees him link up again with Rovers manager Richie Wellens, who the ex-West Ham academy product worked with at Swindon Town.