Juergen Rotors, who heads the city government of Cologne in western Germany, said it had reached an agreement with the Saudis to give King Fahd Academy in nearby Bonn “a fresh start”.
The school will have to confine itself to “its scholastic mission”, he told a press conference in Cologne.
He said it was “a final chance” for the school, which would continue to be “systematically monitored”.
Rotors had previously indicated that his administration wanted to close the academy because of its alleged “fundamentalist” activities. Although the school is privately run and funded, the local authority has oversight rights.
Last week, officials in Cologne said the school suspended a teacher for reportedly urging students to wage a holy war against the West during prayers at its mosque.
According to the weekly news magazine Der Spiegel, German officials feared the school was becoming a magnet for Islamist hardliners, some of whom have been linked to probes by federal prosecutors into the al-Qaida network.
Education officials were also worried it was increasingly emphasising religious instruction over academic studies.
The school will have to confine itself to “its scholastic mission”
The school, founded in 1994, has some 460 pupils up to the age of 18, around 200 of whom have German nationality.
Rotors said he had been “determined” to close the academy until a solution was found “at the last minute” following talks with the Saudi embassy and the German Foreign Ministry.
He said the measures included ensuring German language tuition, restriction of Islamic and any other activities on or off the campus that might encourage hardliners, and allowing access to the mosque to students and staff only.
Staff with connections to hardliners would be replaced, as would those who preached violence or “aggressive fundamentalism”, he added.
Separately, a supervisory committee is to be created to monitor compliance with the measures.
Germany stepped up the tracking of Islamists in the country after the 11 September 2001 attacks. Authorities were embarrassed when it emerged that three of the hijackers, including alleged ringleader Muhammad Atta, had lived undetected in Hamburg, northern Germany, for years.
German Chancellor Gerhard Schroeder expressed his concerns over the school during a visit to Riyadh earlier in October, when Saudi officials promised to review the matter.