Celtic manager Ronny Deila insists Virgil van Dijk does not want to leave the Scottish Premiership leaders in January.
Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Boyd is back in Scotland following spells with Middlesbrough, Nottingham Forest, Turkish side Eskisehirspor and MLS club Portland Timbers, who released him last month, and has signed until the end of the season.
Boyd, who scored 67 goals for Kilmarnock before moving to Ibrox in January 2006, told BBC Scotland: "I've just passed my medical and everything's all done and dusted.
"I'm delighted to be back. Hopefully, I can get some games and we finish as high as possible.
"I've plenty of years left in me yet. It's important I'm playing on a regular basis.
"When you come home you appreciate what you've got and playing at Killie gives me a great chance to play football near my family."
The forward was not registered in time to face Aberdeen in the Clydesdale Bank Premier League but could face Hibernian at Easter Road on Wednesday.
"You're never fully fit until you're playing games and that's what I need," he said. "Hopefully on Wednesday night I can play a part.
"I've been training with Rangers the last two months so I must thank them for that."
Boyd has followed his fellow 29-year-old James McFadden in going back to his first club.
McFadden, who like Boyd last played for Scotland in the 2-1 win over Liechtenstein in September 2010, re-signed for Motherwell on Monday.
Boyd said: "You see Faddy going back and he's probably on a similar boat to me - being settled back at home and playing football.
"You play your best football when you're happy and settled. I'm delighted as this is where it all started."
Boyd could yet return to Rangers when the Ibrox club's transfer embargo ends on September 1 but Kilmarnock boss Kenny Shiels hopes to keep the striker beyond the summer.
Shiels said: "In the first case he's here until the end of the season. Mutually we're hoping to extend that, but we'll see how things go."