The Welsh club signed the 25-year old midfielder from Southampton on a three-and-a-half-year deal for a reported fee of £3million which Monk suggests was not a transfer he thought he would occur this winter.
"I pushed a little bit for him to come in the summer, but it didn't happen because he was committed to Southampton and going forward with them," said the Swans boss.
"But when the opportunity came up again in this window, we were happy to have the chance to bring him in.
"I was surprised a little bit he was available. I understand an offer of a new contract was in place at Southampton, but for whatever reasons he felt he didn't want to sign it.
"He wanted to come here and we have showed the same enthusiasm to sign him, so that's a good recipe."
Monk added that Cork would add plenty of depth to his midfield and was looking to get him going in a Swans shirt as soon as possible.
"He's got good experience at this level and he is a British player which is good," Monk added.
"He has a Chelsea background as well so he has got good pedigree, and he is at a good age to develop into a top midfielder.
"Jack will add to quality we already have at the club and my job is to mould him slightly into what we want to do here."
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