Hartson, Guppy, Sylla and Martin O'Neill
Celtic signed Hartson from Coventry City for £6.5m, despite the Welsh international striker having failed previous medicals at Rangers and Tottenham Hotspur.
Hartson admitted: "The doctor said there is something in the knee, but it might disrupt my training in the distant future - but not in the near future.
"I have no point to prove to Rangers. I was excited at the time, but it didn't happen.
"I got on with my job at Wimbledon, went to Coventry and here now I am here.
Not a gamble
"I am not bitter. I am happy to put on a Celtic shirt."
Hartson is itching to start scoring for Celtic and said: "The earlier I can get the goals the better, because it takes a bit of pressure off, but first I've got to get into the team.
"I know it's going to be tough, because Chris Sutton is in good form, but I've had competition wherever I've been.
Celtic manager Martin O'Neill does not consider Hartson's signing a gamble but conceded that the Welshman still has to beat lingering doubts over his fitness.
"I think there are question marks over a lot of people," said O'Neill.
"There were a number of players last season whose confidence was down and who've got the confidence back and are flying now.
"I didn't sign John Hartson on potential. He's a proven player in the Premiership.
"There are doubts over his fitness, but that's something we'll do our best to sort out."
O'Neill admits that Hartson has a battle on his hands to break up the highly successful partnership of Henrik Larsson and Sutton.
He said: "Larsson and Sutton are a great partnership, but John's here now and he hasn't come up here to play second fiddle.
"We've now got healthy competition and I couldn't be happier."
Great natural talent
O'Neill also explained his thinking in buying Steve Guppy from Leicester City and Momo Sylla from St Johnstone, each for about three-quarters of a million pounds.
"Guppy's an excellent crosser of the ball and Sylla's got great natural talent," said O'Neill.
"Guppy's got to get in the side first. There's plenty of competition in front of him and he knows that.
"He has got to get past Bobby Petta to get in the side.
"I think Sylla can do well. He can play in a number of positions, which is good news for us."