The former Fleetwood Town boss takes over after the exit of duo Anthony Johnson and Bernard Morley last week.
The 46-year-old left Scunthorpe United earlier this year and he says the challenge of taking the National League North champions forward is one he couldn't turn down.
Alexander said: “I was immediately impressed by the scale of the ambition this club and the owners have.
“It has made rapid progress over the last four years and I am delighted they have asked myself and Chris to spearhead the next stage of the club’s development.
“As a manager you have to look for certain aspects of what can be achieved at a new club and the possibilities here are boundless.
“There is a great deal of work to be done on and off the pitch to fulfil the potential of Salford City and I can’t wait to get started. Even though this season has just ended, our work in preparation for the club’s first season at National level will continue throughout the summer.”
Ammies owner Gary Neville believes he has the right man.
“After what happened last week we had to react quickly," he told the club's website.
"Sporting director, Chris Casper, led the process and when he made the club aware of the opportunity to secure someone of Graham’s experience and credibility we moved decisively.
"We have acquired the highest quality of manager in Graham to continue the great work that has been done over the last four seasons. We have had stability at this club and we now look forward to a new chapter with Graham, who has accepted a four year deal."
Casper said Alexander has the makings of a great manager and he is excited that the Preston legend has agreed terms.
“When we met with him, we were impressed with his values, his passion and his drive," the Sporting Director said. "His wealth of experience will certainly benefit Salford as we look to take on the challenge of playing in the National League.
"Graham will be joined by Chris Lucketti and we are delighted to have someone of his credibility joining the team also. This appointment is exciting and we can not wait until the start of the new season.”
PHOTOS: SALFORD CITY FC