They have a regulatory eight weeks to respond in writing to the arguments filed by Buhari and Abubakar.
The opposition wants the final tally to be disregarded and another election to be held.
An election tribunal ruled earlier this year that Buhari and Abubakar had failed to prove that fraud was so pervasive that the official results should be discarded.
Buhari, a former military ruler who was placed second in the election, filed his case for seeking the annulment on Monday.
Abubakar, a former vice-president who came third, is due to file his on Friday.
The case is likely to drag on for several months because once Yar'Adua has made his case, Buhari and Abubakar have a further three weeks in which to reply.
Yar'Adua, who was not involved in setting up the balloting, has acknowledged voting deficiencies and has ordered his administration to strengthen electoral practices.
The seven-judge bench of the supreme court hearing Buhari and Abubakar's petition goes into recess in July and only resumes in September, lawyers said.
Many Nigerians say the 2007 election was the worst-run in the country's 48-year history since independence from Britain.
Nine governorship elections which were held a week before the presidential ballot have been overturned and two new races run.