The defender left Dundee as a free agent just minutes before the transfer window slammed shut. The 26-year-old activated a clause in his contract allowing him to leave Dens Park in search of a new challenge.
The one-time England cap was linked with a move to Russia in 2017 after leaving QPR, with Lokomotiv Moscow reportedly interested, but the proposed move failed to materialise.
Caulker joined Dundee in February 2018, with the Dark Blues becoming the ninth club of his career.
• READ MORE - Steven Caulker leaves Dundee by mutual consent
After starting out with Tottenham, and following loan spells at Yeovil, Bristol City and Swansea, he joined Cardiff, before transferring to Queens Park Rangers a year later.
While at Loftus Road he was sent on loan to Southampton and Liverpool, before he left QPR by mutual consent in December 2017.
Caulker was linked with Celtic but the player turned down the move, admitting that dealing with depression, and battles with alcohol and gambling had left him mentally unready to play for a club of Celtic’s stature.
Rosenborg submitted a £2 million offer for the player in April this year but having recently lost Jack Hendry to Celtic, Dundee rejected the bid and Caulker remained on Tayside.
The current manager of Arsenal Kyiv is former Dundee and Middlesbrough forward Fabrizio Ravanelli, and the team - who won the Ukrainian second tier title last season - plays its home matches at the 5,654-capacity Kolos Stadium in Boryspil.