Solskjaer expects the pair to join his squad for training in the north west ahead of their Barclays Premier League game at Manchester United, although it is not thought they will be eligible to play.
Defender Fabio, 23, will join the club from United, Solskjaer's old side, while 29-year-old striker Jones will arrive from Stoke.
There has been no confirmation yet of whether forward Peter Odemwingie will be joining Stoke in return, as expected.
Solskjaer, speaking at a press conference in Manchester, where his team have been based since their FA Cup tie at Bolton last weekend, said: "Fabio and Kenwyne will join training today. I have just met them downstairs and that is more or less done."
Solskjaer, appointed on January 2, has already signed three players this month in Magnus Wolff Eikrem, Mats Moller Daehli and Jo Inge Berget.
Another player from United, winger Wilfried Zaha, is likely to join them in the next day.
Solskjaer said: "Everything is not complete so we cannot confirm that.
"We hope to get that done in the next 24 hours or so, so he can be ready for the weekend."
Those deals are likely to bring an end to Cardiff's business during the January transfer window.
Solskjaer has been keen to strengthen the squad he inherited from Malky Mackay - who had been told there was no money to spend - as the relegation battle intensifies.
Cardiff head to Old Trafford bottom of the Premier League having not won any of their last six games in the competition.
Solskjaer said: "You never know with ins and outs but I think that is me concluded."