I am on OPT and H1 got approved, Can I transfer my H1 immediately to another employer

[PM01070107]

I am working for x employer and y client since 3 years on CPT and OPT. Now my H1 got approved. My Client offered me a full time position. Can transfer H1 to my Client immediately.( H1 approved on Dec 20, 2017 and Full time offer with client available from jan 1st 2018). Your suggestions are very valuable to me.