The former Celtic defender was on his way to get his hair cut last week when former team-mate Lennon called after being promoted to interim manager at Parkhead to ask if he would like to be his assistant.
Mjallby, who made 144 appearances for Celtic between 1998 and 2004 after being signed by Jozef Venglos, was forced into an immediate answer but was delighted to make his return to Glasgow the next day.
"It's brilliant to be here, of course," Mjallby said.
"The Celtic supporters will always have a big place in my heart, so when Neil phoned me in the afternoon and told me I had one minute to decide it was quite simple to say yes, even if I didn't know much about what he wanted me to do.
"I packed my bags and organised my flights and now I'm here.
"Obviously, over the years I have met Neil at different functions and at different games here at Celtic Park and we have always talked about it.
"If he came across a job as manager, then he would ask me to go along with him and work with him.
"In the end it came out of the blue, but it was an easy decision – should I go and get my hair cut or join Celtic?"
Last week's 4-0 defeat at St Mirren ended Tony Mowbray's short tenure as Celtic manager, with assistant Mark Venus and first-team coach Peter Grant also leaving the club.
Lennon and Mjallby made an instant impact as Celtic charged to a 3-1 home win over Kilmarnock at the weekend.
The Swede, who scored 13 goals during his career at Parkhead before leaving for an unsuccessful stint in Spain, is looking to build on that encouraging victory in the closing weeks of the season where the only realistic hope of silverware comes in the Active Nation Scottish Cup. Celtic are due to meet Ross County in the semi-finals at Hampden a week on Sunday.
"The players are here to perform and do a job," said Mjallby.
"We need to get the team back to winning ways and develop a winning mentality, which Neil and I both had on the pitch and in the dressing room here at Celtic.
"Hopefully we can at least get our message across to the players and get a wee bit more organised at the back as the players are good enough to perform and get results – I am sure of that.
"When the confidence is not really there, there will always be pressure at a big club.
"You are here to win trophies and it hasn't gone well this season, but hopefully we can finish off well and see what happens."