Explain how Rome officially becomes in empire?

It largely depends upon your definition of 'empire'. If you mean 'empire' to mean an autocratic state, then it began when Octavian Caesar (a. k. a. Augustus Caesar) became the first emperor of Rome in 27 BC. The transition from republic to empire in that sense didn't just happen overnight however.

It began when Octavian Caesar became the first emperor of Rome in 27 BC.