Kenya, renowned for its distance runners, has faced frequent allegations of doping with about 40 cases reported in the past four years.
The International Olympic Committee said on Tuesday that competitors from Russia and Kenya, given their countries' recent history of doping, would have to be screened individually before being allowed to participate in the Rio Games.
"We look forward to WADA's review and declaration of Kenya as compliant with existing rules," President Uhuru Kenyatta said after signing the amendments into law. "Kenya has always supported clean sport and will continue to do so."
WADA declared Kenya non-compliant with its anti-doping code, prompting the country to introduce new legislation.
After WADA still found flaws, such as the presence of government officials in Kenya's anti-doping agency, Kenya began working on amendments.
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Kenyan officials said last week that WADA had approved the amendments to prevent doping by Kenyan athletics.
"The president instructed me to ensure all athletes going to the Games are screened and the results reported to him personally," National Olympic Committee of Kenya (NOCK) Chairman Kipchoge Keino told Reuters after the signing.
"We must fight doping and all forms of cheating in sports and Olympic movement," said Keino.
Among the high-profile Kenyan athletes who have failed doping tests was former three-time Boston City and Chicago marathon winner, Rita Jeptoo.
(Additional reporting by George Obulutsa; Writing by Edmund Blair; Editing by Dominic Evans/Sudipto Ganguly)
