Solanke arrived ahead of Tottenham's 3-2 preseason friendly defeat to Bayern Munich.
Postecoglou later said of his new striker: "He was obviously one I was very keen to get in. It took a while to get it over the line but I think he will be a great fit for us in terms of the player he is and the point of his career where he is at. I think he will be a good fit. As I said, we are a bit light in that front third in terms of adding quality not just to the squad but also to our team. He certainly does that. Pleased to get him on board and we have a week and a bit to work with him.
"We identified him because he has the attributes we are looking for in terms of our position. He gives us some things we probably have been missing in the last 12 months, particularly when Richarlison was out last year. When Richy played he was very effective for us, it was quite evident when he was out we didn’t really have a player who can make the impact Dom can in the final third and just with his general play. So I think he will be a good fit for us.
"We have got him at a really good time in his career. He has had to work his way back up which I always think is a good thing. Sometimes when careers go smoothly you wonder how people will handle setbacks but he had setbacks earlier in his career. He has fought his way back and has become a really good Premier League striker now. He is really keen to push on. He wants to improve and make an impact. I think it’s a great time for us to bring him in."
On seeing off rivals for the former Bournemouth striker, Postecoglou continued: "Yeah I think it’s important. Players certainly have options out there and you kind of want to understand the motivations for why a player would want to come to us. Since I spoke to him I got a real sense he had a really burning desire to take his football to another level and really challenge himself at a big club. Like I said, he is keen to make an impact and our job is to make sure we provide that platform for him."
Postecoglou admits he's been following Solanke's career.
"Yeah, a fair while, but again, you kind of look at players who've had, like I said, interesting journeys and with some players, things happen really early in their careers and they go really well, but then there's inevitable stumbles along the way and you want to see how they react.
"But Dom had a very bright start to his career and he was at big clubs, which every player aspires to, but for one reason or another, it didn't work out for him, but the fact that he's got himself back to this position where he's again one of the premier strikers in the Premier League, it's a testament to his character and he's only 26, about to turn 27, so I think probably because of those early challenges he had, I think he's going try to push and have a really strong and impactful, meaningful years from now on."
On whether Solanke will face Leicester City for their Premier League kickoff, he added: "Yeah, I don't see any reason why he shouldn't be. He's played most of the preseason. Slight knock in the last game Bournemouth played, but, of course, we'll have a look at him during, during the week. But I think that considering he's done most of the pre-season, I see no reason why he wouldn't be available."