@olliegen It's less of a case of how long it will take and more a case of what it will take.
In the sense that it would be virtually impossible to tell you how long it would take because there's too many variables that make that impossible to guage; such as diet, body composition, workout regime, intensity and frequency of diet, basal metabolic rate, etc, etc.
I can give you a vague breakdown of what it will take to achieve a physique like that, and that's dedication and discipline. It will take more than just pull ups and pushups to achieve a physique like that, they mainly build lats and pecs. What it will take is for you to train in the gym 3-4 times a week for 1-2 hours at a time, you will need to do some resistance training (weights and machines) that target the muscles you're looking to build. You will also need to incorporate some cardio, as your desired physique has much lower body fat than what you currently have and resistance training does not burn fat, a low sugar diet and a good cardio routine is the only effective way to lose excess body fat. You want to make sure you're eating a lot of protein and avoiding alcohol, as alcohol destroys muscle recovery.
Train consistently and put the right things in your body and eventually you will start to see the changes you're hoping for. It won't happen right away, I can't tell you when it will happen but it will happen eventually, it is impossible to exercise regularly and consistently and eat the right diet and see no progress at all. I'd say give it six months, you most likely won't have your desired body but the progress will become apparent, and that will motivate you to keep going.