It is permitted by the Quran, the sunnah, and scholarly consensus.

As for the Quran, Allah the Exalted says:

“Wipe over your heads and your feet up to the ankles.” [al-Ma'idah 5:6]

This is according to the genitive reading.

As for the sunnah, hadiths concerning this have been transmitted from the Prophet, peace and blessings be upon him, through multiple uninterrupted chains.

The poet said:

Among the reports transmitted through multiple uninterrupted chains are: “Whoever lies,”
“Whoever builds a house for Allah, seeking His reward,”
the Beatific Vision, intercession, the Basin,
and wiping over leather socks—these are but some of them.

Imam Ahmad, may Allah have mercy on him, said: “I have no reservation whatsoever concerning wiping; there are forty hadiths concerning it from the Prophet, peace and blessings be upon him.” (1) That is, I have not the slightest doubt regarding its permissibility.

As for scholarly consensus, Ahl al-Sunnah are agreed, in general, on the permissibility of wiping over leather socks.

“It is permissible for a resident for one day and one night …”

His statement, “It is permissible for a resident for one day and one night,” is phrased