Jannik Sinner won the year's first Grand Slam and his third overall at the Australian Open in January
The 23-year-old Italian, who last month won the Australian Open, is suspended from 9 February until 4 May.
He will be eligible to play in the year's next Grand Slam event, the French Open, which starts on 19 May.
Wada had launched an appeal to the Court of Arbitration for Sport (Cas) over the 2024 decision by the International Tennis Integrity Agency (ITIA) not to suspend Sinner.
Wada wanted a ban of up to two years but on Saturday said it accepts his explanation that he was inadvertently contaminated with the banned substance clostebol by his physiotherapist, and the case will now not take place.
The body explained it accepts the three-time Grand Slam champion "did not intend to cheat", that the drug "did not provide any performance-enhancing benefit" and this happened "without his knowledge as the result of negligence of members of his entourage".
It added: "However, under the code and by virtue of Cas precedent, an athlete bears responsibility for the entourage's negligence. Based on the unique set of facts of this case, a three-month suspension is deemed to be an appropriate outcome."
In a statement released by his lawyers, Sinner said: "This case had been hanging over me for nearly a year and the process still had a long time to run with a decision maybe only at the end of the year.
"I have always accepted that I am responsible for my team and realise Wada's strict rules are an important protection for the sport I love. On that basis I have accepted Wada's offer to resolve these proceedings on the basis of a three-month sanction."
Tennis has seen some high-profile doping cases over the past six months, with leading female player Iga Swiatek accepting a one-month suspension in November after testing positive for a banned substance when she was world number one.
Sinner had previously been cleared of any wrongdoing by an independent panel after testing positive for clostebol in March 2024.
It had accepted that he had been inadvertently contaminated by his physiotherapist, who was treating a cut on his hand with an over-the-counter spray, which was later found to contain the banned substance.
The ITIA said in August that the panel found Sinner bore "no fault or negligence" for testing positive for low levels of a metabolite of clostebol - a steroid that can be used to build muscle mass.
But Wada lodged an appeal with Cas last September, stating at the time that the finding of "no fault or negligence" was not correct under the applicable rules.
It sought a ban of between one and two years, with a hearing scheduled for 16-17 April.
But Sinner has now accepted the three-month ban and the next tournament he can play in is the Italian Open, which begins on 7 May.
He will miss prestigious hard-court tournaments in Indian Wells and Miami in the US, plus many of the clay tournaments that build up to the French Open.
Wada, which has officially withdrawn its Cas appeal, says Sinner can return to "official training activity" from 13 April.
The ITIA says Wada's outcome supports its initial findings.
