Grading: (2) Its chain is "sahih".

Reference / Source: It was narrated by al-Bukhari in "al-Tarikh al-Kabir" (8/ 417) in suspended form (ta'liqan), 'Umar bin Shabbah in "Tarikh al-Madinah" (3/ 1053), al-Tabarani in "al-Kabir" (12816) and "al-Awsat" (929, 5223), Ibn 'Abd al-Barr in "al-Isti'ab" (p. 411) and al-Diya' al-Maqdisi in "al-Mukhtarah" (9/ 507, 508), through various routes from Sa'd bin Sulayman al-Wasiti, with this chain.

Reference / Source: Bahshal narrated it in "Tarikh Wasit" (p. 77) from 'Umar bin Ahmad bin Salih bin Ziyad, from 'Abbad bin al-'Awwam, with this chain.

Corroborating chains and supporting reports: A similar narration is established from Anas bin Malik (may Allah be pleased with him) in al-Bukhari's "al-Adab al-Mufrad" (568) and elsewhere with a "sahih" chain.

Important point: This (the brotherhood between al-Zubayr and Ibn Mas'ud) is what is "sahih", contrary to the statement of Ibn Ishaq, who said that the Prophet (peace and blessings be upon him) established brotherhood between al-Zubayr and Salamah bin Salamah bin Waqsh.
Technical note / Defect ('illah): It also refutes the statement of Mus'ab bin 'Abdullah al-Zubayri which Ibn Abi Khaythamah quoted in his "Tarikh" (second part: 2837): "I do not know of this brotherhood between al-Zubayr and 'Abdullah."
Details of the narration: See hadith number (8204), which indicates that al-Zubayr bin al-'Awwam was made a brother to Ka'b bin Malik al-Ansari. Bear in mind that that was the brotherhood (mu'akhah) of "Madinah", established between the Emigrants and the Helpers, whereas the present narration concerns the brotherhood of "Makkah", as will be explained there.