Defender Taylor has signed a one-year contract with Steve Bruce’s side, having been released by Newcastle at the end of last season.
Midfielder Clucas, 24, has agreed a three-year deal after joining for an undisclosed fee from League One Chesterfield.
30-year-old Taylor was a free agent and was reportedly holding talks with Bolton Wanderers, Nottingham Forest and Belgian side Standard Liege.
Taylor has been signed by Bruce to shore up a Tigers defence that conceded 51 goals on their way to relegation from the Premier League last season.
The former England U-21 player tweeted: “Delighted to have signed for @HullCity. I’m now looking forward to getting started. Thanks for the kind messages and here’s to a great season.”
Taylor’s time at Newcastle was plagued by serious injury problems which started when he suffered torn cruciate ligaments in his knee in 2012 and spent 26 months on the sidelines.
He returned to action in October 2014 before injuring himself again against QPR the following month.
However, Taylor returned in February 2015 to help the side avoid relegation before being released in acrimonious circumstances at the end of the season.