It is also understood that talks are continuing over French duo Remy Cabella and Bafetimbi Gomis.
Sunderland midfielder Colback has been in talks with a number of clubs since the end of the season, but Newcastle were always his preferred destination and they have now finalised terms with the player.
Colback is expected to undergo his medical shortly, and the 24-year-old will sign a long-term deal on Tyneside.
Like with Colback, the deal for Perez has been expected and Newcastle have also been working on that for a number of weeks.
Perez is currently with Tenerife in Spain, but he has a release clause of £1.8million which Newcastle have already agreed to meet and the 20-year-old, like Colback, is expected in the North East to complete the formalities of his move in the coming days.
Newcastle's penchant for the French market - though - will also continue and Sky Sports understands that talks with Montpellier are now at an advanced stage over Cabella - who is currently with the French squad as he is one of the stand-by players for the World Cup.
Newcastle tried to sign the 24-year-old in January, but he was committed to helping Montpellier avoid relegation before leaving, However, he was quick to confirm he would be leaving once the Ligue 1 season had finished.
Sources have told Sky Sports that Newcastle are yet to lodge an official bid, but the two clubs are closing on a deal which could be worth up to €10million.
A possible fourth deal is another familiar name to Newcastle fans, and is French striker Bafetimbi Gomis - who is available on a free transfer from Lyon.
Newcastle have long been fans of the 28-year-old - who had seemed set for a big-money move to Turkey.
However, he has seemingly decided England is where he wants to be and Newcastle are believed to be in pole-position to land Gomis - who had previously priced himself out of a move to Tyneside.
But after talks were reinitiated by Gomis' representatives, Newcastle are close to landing one of their long-term targets.
Newcastle also remain very interested in Hertha Berlin striker Pierre-Michel Lasogga, but one player they are not going to move for is Leeds' Ross McCormack.