The long-awaited sale, which was flagged by Mirror Group earlier this month, puts Granada ahead of its rival ITV broadcasters, Carlton and United News and Media, in the race to take control of SMG.
Granada paid 915p per share for the stake, an 8 per cent premium to SMG's closing share price on Monday. News of the sale lifted SMG shares 22p to 865.5p yesterday.
Although rules governing the amount of television advertising that can be controlled by a single broadcaster currently prevent Granada from bidding for SMG, buying the stake allows Granada to block its rivals from mounting a bid while waiting for the rules to change.
The Government is coming under increasing pressure to ease the ownership restrictions on ITV companies as Channel 3 faces competition from the exploding number of digital channels. However, the law is unlikely to be changed before the next election.
Although Granada said it had "no present intention" of bidding for SMG, it said it reserved the right to change its stance if another group built a stake of more than 15 per cent.
This means that Granada will be free to bid if one of its rivals buys the 18.6 per cent shareholding in SMG owned by Flextech, the supplier of television channels. Flextech - which is expected to report a pre-tax loss of around pounds 5m when it reports full-year results today - is thought to have been in talks with a number of potential buyers about selling the stake. CanWest, the Canadian broadcaster, is believed to be interested in taking a stake.
Analysts said the situation was similar to the takeover of Yorkshire Tyne-Tees Television in 1997, when Granada gradually built a 29.9 per cent stake in the ITV broadcaster before finally launching a full bid.
John Allwood, Mirror's chief executive, welcomed the deal. "It's great news for Mirror Group," he said. "It's clean, and it gives us the money."
Mirror has talked to a number of potential buyers about the shareholding, but settled for Granada because it was offering an immediate deal. Other options are thought to have involved buying both Mirror and Flextech's stakes as a launch-pad for a full bid for SMG.
Under the terms of the deal, if Granada sells on the stake in the next 12 months it will have to pass on any profits it makes to Mirror.
Combined with the sale of the former headquarters in Holborn for pounds 40m, which was announced last week, Mirror has reduced its debt load by pounds 150m in the space of a few days.
In a related development, the Independent Television Commission yesterday rejected a claim by British Sky Broadcasting that ITV should be forced to supply its new channel, ITV2, to the satellite broadcaster's platform. ITV2 is currently only available on ONdigital, the broadcaster jointly owned by Granada and Carlton, and cable television.