Swansea will pay up to £5m – plus Taylor – for the Ghana international who has signed a three-and-a-half year deal at the Liberty Stadium.
Ayew is the brother of former Swansea forward Andre Ayew.
“He is a very good acquisition. He’s versatile and dynamic to attack the lines and get in behind defences.
“He will certainly give us something different to what we’ve got.”
The 25-year-old Ayew, whose brother Andre played for Swansea last season before joining West Ham for £20.5m, is currently with Ghana at the Africa Cup of Nations.
Taylor, 27, has made more than 150 appearances for the club since his arriving from Wrexham, who could still receive a cash windfall through a sell-on clause.
His departure ends a six-and-a-half year association with the Swans.
The left-back moved to the Liberty from non-league club Wrexham in 2010 and played for the Swans 179 times.
“Neil has been a great servant for this club. I had a really nice discussion with him about his position,” added Clement.
“He said he wanted to take this opportunity and I supported that. It’s the right time for him to have a new challenge and we wish him all the best.
Elsewhere, a potential loan move for Benfica defender Lisandro Ezequiel Lopez will not happen.
Meanwhile, the club’s Dutch striker Marvin Emnes has rejoined Blackburn on loan.