The fast bowler last played for the national side in a Test match against Sri Lanka in November last year at Kingsmead but suffered a groin niggle in the game.
The damage was greater than initially expected and Coetzee was ruled out for most of the SA20, returning to play a single match for the Joburg Super Kings before frustratingly suffering a hamstring injury.
A return was on the cards ahead of the ICC Champions Trophy in February but the paceman had more tightness in his groin and was not risked for the 50-over tournament in Pakistan.
The 24-year-old made his comeback to the field by playing four matches for the Gujarat Titans in the Indian Premier League (IPL) and then, more recently, five games for Seattle Orcas in Major League Cricket.
Speaking to the media from Harare, Coetzee said: "I'm feeling really good. I'm very happy to be back at the Proteas. It's been a while and I've obviously been working towards that ever since I left, so I'm excited to go do my best.
"I think what I do for a living, being a fast bowler, I think I've come to understand what happens to us. And it has been a tough few months. But I'm not someone who stands out in that sense.
"I think if you look at the landscape of all the bowlers who bowl high 140s, you know, we all struggle with injuries occasionally. So it's been tough, but I understand the process. I understand what it requires."
An interesting dynamic in the upcoming series is that former Proteas white-ball head coach Rob Walter will be in charge of New Zealand for the first time.
It will also be Shukri Conrad's first assignment as South Africa's coach in the shorter formats having taken over the reins from Walters.
Coetzee added: "In the landscape right now, you play under different coaches all the time, so I think seeing him (Walter) you just say 'hello'. We get on well and I'm happy for him to have a good job."
Proteas captain Temba Bavuma spent valuable time in the middle ahead of the Test series in India after scoring a fifty in South Africa A's record run-chase against India A in Bengaluru.
The Proteas suffered a calamitous batting collapse as Pakistan claimed a seven-wicket win in the third and final ODI in Faisalabad on Saturday and with it a 2-1 series victory.
Quinton de Kock produced a batting masterclass as South Africa crushed Pakistan by eight wickets in the second ODI in Faisalabad, chasing down 270 with nearly 10 overs to spare to level the three-match series 1-1.
The Proteas fought to the bitter end but ultimately fell to a two-wicket defeat with two balls to spare against Pakistan in the first ODI in Faisalabad on Tuesday.
