My Son and his mother live in my home and I pay for the house,electricity,food, phone, etc I plan to claim Head of House Can he still be a dependent on my taxes and hers

You cannot have Head of Household filing status if you are not going to claim a qualifying person as a dependent on your tax return.

You are confusing the rules that can be used for divorced or never married parents who live apart and share custody.  If all of you are living together as a family, then those rules and the "signed agreement" do not apply to your situation.   Only ONE of you can enter the child on your tax return and get the child-related credits.  

One of you files as Single ----with no mention at all of the child on your tax return. The other parent claims the child and the child-related credits including earned income credit, childcare credit, child tax credit----and possibly Head of Household if they paid for over half the support of the household.

If you are not sure which of you that should be--use the IRS tiebreaker rule.

TIE BREAKER RULES

https://itap1.for.irs.gov/owda/0/resource/Commentary_Files_Redirect_ITA/en-US/help/tbrk09.html

If you each try entering the child on your returns, one of your e-files will be rejected.