The national press ad tells readers that the studio's laser therapy technology and "strand-by-strand" procedures can "provide most with a guaranteed full and natural looking head of hair again".
Warne was pictured saying: "I stopped worrying about my hair when I heeded the Warne-ing signs and saw Advanced Hair Studio".
Additional text states that Warne uses the "Advanced Hair and Scalp Fitness Program".
A series of four photographs also showed the scalp of Gooch before and after treatment at the studio, alongside text that said: "Graham Gooch UK cricket legend received the strand-by-strand replacement procedure".
The Advertising Standards Authority received a complaint from a consumer arguing that the ad misleadingly implied that the studio's treatment could stop hair loss or cause hair to regrow.
The complainant also questioned whether claims that the laser therapy had official clearance were misleading.
Advanced Hair Studio said the ads offered two solutions to hair loss and said it had not meant to imply that the laser treatment reversed hair loss, but provided a cosmetic improvement.
AHS also pointed out that the strand-by-strand procedure did result in a fuller head of hair.
However, the ASA upheld the two complaints against the firm for implying the effects were more than cosmetic and warned that the ad should not appear again in its current form.
It is not the first time that an Advanced Hair Studio ad has fallen foul of the ASA. The watchdog has upheld several complaints about various AHS ads in the past.
Carl Howell, founder and chairman of Advanced Hair Studio, said: "It is frustrating, if not baffling, when you have followed the advice of CAP (Committee of Advertising Practice) and the ASA to get a result like this.
"We ensured that the particular advertisement met the code of compliance and received approval to advertise. Our advert was also approved by the ASA in its first adjudication.
"This process, initiated by one unidentified complainant, has taken over two years to resolve and the initial decision in our favour was overturned without any further new arguments presented against us.
"This is not the first time that our advertisement has been approved, only to be ruled against by the same body later. What is an advertiser to do?
"Regardless, we will continue to consult with CAP and the ASA as Advanced Hair Studio's programmes and procedures provide a range of very successful solutions for people suffering from hair loss."