Aston Villa, Dundee United, St Mirren and Hamilton Accies were all keen on securing the 17-year-old right-back's services, according to head of youth Anderson.
But after joining the Ton's under-17s on trial towards the end of last season after the club was recommended to Eadie by Parkhead youth chiefs, he decided to sign on at Cappielow.
Anderson said: "The boy Glenn Eadie was referred to us by Celtic. Apparently they have told players who have left them to try Morton because we are doing things the right way.
"Glenn had opportunities to go to Villa, Dundee United, Hamilton and St Mirren. But I spoke to his dad, telling him about Hoppy [David Hopkin] being in charge of the development squad and our plans.
"He's been up at Celtic for three years and and his signing is a big coup for us.
"There was another lad, Mark Barrowman, who was also told by Celtic to go to Morton because he'd get an opportunity down here.
"He's a left sided centre-half who has played for Scotland at various youth levels. I believe he's been down at Tottenham and Everton on trial and it doesn't look like we'll get him. But his agent knows we're interested."