Former striker Curtis, 58, who scored 95 goals in 359 league appearances for the Swans, had previously worked with the reserves and the club's young professionals.
But with former midfielder Kristian O'Leary returning to the Liberty Stadium to take on those duties, Curtis has been handed greater responsibility by new manager Laudrup.
The former Wales international will now work alongside Laudrup's assistant Erik Larsen as first-team coach.
"Alan will work closely with Michael on all first-team matters,'' said chairman Huw Jenkins.
"He will help provide the continuous link to what we have developed at this football club over the last few years.
"Alan will help provide Michael with the knowledge of not only the existing squad and his experience of life in the Premier League, but how things have run at the club over the years.
"It will help make Michael's transition into our football club as efficient, effective and comfortable as possible.
"Alan's reputation as a coach and a person is right up there with the best and we would be foolish not to utilise his talents. He has been a fantastic servant to this football club - and long may that continue."
Source: PA
Source: PA