Tourist Visa to Spouse visa

My tourist visa expires late december and I want to stay here longer to help my wife move while waiting her green card in the states. What is the process for doing this and do I have enough time left? if I have to leave the country I can. I am currently on holiday for work and they said they are good taking as much time as I need as my wife just had our first child a month ago.

for completeness I am a US citizen and we have been marred for 4 years. and lived together for 3 of those 4 years.

Any help would be greatly appreciated.

by Staracer67