My nephew lives with us. He has full time job, pays no rent, “bills”, etc. He files his own tax’s. Here is my question, can I Claim him on income taxes?

No.  The full time job disqualifies him as a dependent, regardless of the amount of support you provided.  If he was also a full time student, under age 24,  the answer might be different.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status,  a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each. There is an income limit (only $4200 for the whole year) for a standard dependent.

See full rules at 

https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html