We Don't Know
We know the wights can at least scream as we saw in Season 7 Episode 6, "Beyond the Wall".
From this answer sourced from the wikia they use a language name Skroth. Though the language was never used on screen at the time of it's naming.
The credits for episodes of Season 1 of the TV series include the statement: "Dothraki, Ashai'i, and Skroth languages created by the Language Creation Society and David J. Peterson."
Peterson developed a spoken language for the White Walkers to use in Season 1 (probably in the unaired pilot episode), but it was not ultimately used on-screen, and dropped entirely from Season 2. Instead, actual ice-cracking sound effects were used when the White Walkers are conversing.
In an interview with Entertainment Weekly during Season 2, Executive Producers David Benioff and D.B. Weiss stated that "Skroth" is indeed the official name of the language used by the White Walkers.
In Season 2 Episode 10, "Valar Morghulis" we do see a White Walker use hand signals as it passes Sam. It screams/shrieks too so this could be confirmation of it speaking in Skroth.
However, it appears that Skroth was scrapped though there are conflicting statements.
Also, the information on Skroth there [Wikia] is wrong. I created something for the White Walkers initially called Skroth, and I believe they didn’t end up using it. And that was for season 1; I didn’t do anything for it for season 2.
— David J. Peterson, "Ei Mahrazhi’th Drivoe", Dothraki.com
This answer over on Sci-Fi goes into detail of the books of how the agreement could have come about though it boils down to we don't know. As for the show, well we have even less information so we don't know at all.