Did Muawiyah ibn Abi Sufyan become the ruler of Muslims in a legitimate way?

Muawiyah ibn Abi Sufyan ruled Islamic Caliphate from 661 till 680. Did he come to the power in a legitimate way (according to Quran and hadith)? I am only interested in the views of Sunni Muslim scholars. Please support your answer using accepted references (and explicitly state the school they belong to if they are not generally accepted by Sunni scholars).