Praise be to Allah.
It was proven that the Prophet (peace and blessings of Allaah be upon him) prayed Witr in different ways. He prayed one rak’ah, and three, and five, and seven, and nine. And he prayed three rak’ahs in two different ways, either continuously with one tashahhud, or saying salaam after two rak’ahs and praying one rak’ah and saying salaam after it. He did not pray it like Maghrib, with two tashahhuds and one salaam. Rather he forbade doing that, and said: “Do not pray Witr with three rak’ahs like Maghrib.” Narrated by al-Haakim, 1/403; al-Bayhaqi, 3/31; al-Daaraqutni, p. 172. Al-Haafiz ibn Hajar said in Fath al-Baari (4/301): Its isnaad fulfils the conditions of the two Shaykhs (al-Bukhaari and Muslim).
Shaykh Muhammad al-Saalih al-‘Uthaymeen said:
It is permissible to pray Witr with three rak’ahs, or with five, or with seven, or with nine. If a person prays Witr with three, it may be done in one of two ways, both of which are prescribed in sharee’ah:
1 – Praying the three rak'ahs continually with one tashahhud.
2 – Saying salaam after two rak’ahs, then praying one rak’ah on its own.
Both of these are narrated in the Sunnah, so if a person does it one way sometimes and the other way sometimes, that is good.
It is permissible to say it with one salaam, but it should be with only one tashahhud and not two, because if he does it with two tashahhuds, it will be like Maghrib prayer, and the Prophet (peace and blessings of Allaah be upon him) forbade making it like Maghrib prayer.
Al-Sharh al-Mumti’, 4/14-16