Alexander played under Barry Fry at Barnet and left the Imps this month after guiding them to four successive play-offs, only to be unsuccessful each time in the knockout stages.
In the press conference it was revealed that Fry looked at Alexander last year when the position was avaliable but was put off by Lincoln's compensation demands. that time round it was given to Mark Wright (now at Chester City).
Fry also interviewed ex-Torquay boss Leroy Rosenior for the position but decided to go for Alexander who "performed miracles at Lincoln, getting them into the play-offs every year on a limited budget".