Professor wrote to me saying he supports my fellowship application to the committee
It is positive certainly, but not definitive. It is just a progress report sent as a courtesy. He is being encouraging, but not making any commitments. 

Of course, you need to go through the normal admissions process. This isn't a substitute for any formal procedures that are required. In US institutions admissions is handled by the university, not the individual professor. Funding may be under his control, however.