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The Coca-Cola Championship club had been linked with the player since the turn of the year and Kelly had admitted he may have to leave White Hart Lane in order to get regular first-team football.
Kelly made just 10 appearances for the north London club last season after coach Martin Jol's preference for Paul Stalteri restricted the 22-year-old to a bit part as Spurs just failed to claim a Champions League spot.
Blues targeted Kelly as a replacement for Mario Melchiot who left the midlands at the end of last season following relegation.
The Dublin-born player admitted he was enticed by the possibility of regular first-team football as he looks to establish himself in the Republic of Ireland side after making his debut earlier in the summer.
'I was at Tottenham from the age of 16 and played over 40 games but things didn't work out the way I wanted,' continued Kelly.
'It was time for me to move on and this is a great opportunity for me to come and play and do well.'
Kelly will join fellow new arrivals Cameron Jerome and Neil Danns as they look to make an immediate return to the top flight.