The Scotland under-21 was reportedly a target of Millwall and has previously been linked to Hibs.
Alexander made two signings on deadline day with another to be confirmed and also secured Stephen O'Donnell on a contract extension.
"For me the biggest bonus is keeping our best players in the building," he said. "We knew there was a possibility of them leaving.
"We turned down substantial bids for Allan Campbell in January.
"We brought in a little bit of experience with Eddie Nolan and Jordan Roberts and there's another young player on his way."
O’Donnell’s short-term deal with the Steelmen expired at the end of January but the Scotland defender elected to stay at Fir Park ahead of the summer’s European Championships.
Steven Lawless re-joined to the club earlier in the month and Harry Robinson as returned from loan at Queen of the South.