Can I claim a 16 month old that has lived in my home since he was born. He not biological mine. His biological father claimed him last year.

[Hal_Al · Accepted solution]

A great aunt is considered "closely related". The child  is your  "Qualifying Child" dependent, because he has lived with you more than half the year. You may claim the Child Tax Credit and the earned Income  Credit, based on that child (if otherwise qualified).
The only conflict would be if he also lived with one of his parents for more than half the year. That does not appear to be the case since you say "neither the custodial parent or the non custodial live with me".

You do not need legal guardianship to claim him, since you are closely related.

.A child closely related to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:
1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or  is totally & permanently disabled
2. He did not provide more than 1/2 his own support
3. He lived with the relative (including temporary absences) for more than half the year
4. He is younger than the relative (not applicable for a disabled child)
5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child, if the child also lived with the parent more than half the year)
6. If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child.
https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...

[Texas Roger]

There are two types of dependents--qualifying child and qualifying relative. You cannot claim the child as a qualifying child dependent because the child is not related to you. You may be able to claim the child as a qualifying relative if the child meets these tests:

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.

2. The person either (a) must be related to you or (b) must live with you all year as a member of your household. 

3. The person's gross  taxable income for the year must be less than $4,150 in 2018.

4. You must provide more than half of the person's total support for the year.

5. The person must be a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico.

NOTE: This answer is not correct based on the additional information provided in comments by the poster.

[Hal_Al]

"You cannot claim the child as a qualifying child dependent because the child is not related to you".

One exception: if you are married to the biological parent, the child is your step child and that is considered related, for tax purposes. You may claim the child as a qualifying child whether you file Married Filing Separately or Married filing jointly.

 Only a Qualifying Child dependent qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit.

[Hal_Al]

We need to know more about the living situation, and the income of the two parents; but here's the basic math;
1. You only get a $500 dependent credit for claiming the child (assuming you're not the legal step parent or otherwise closely related)
2. The non custodial parent (the biological father) gets $2000 for claiming the child
3. The custodial parent (if she has sufficient income) gets up to $5400. But, if the custodial parent had sufficient income, and lived with you and the child, you would not be allowed to claim the child at all (the qualifying child of another taxpayer rule)

[girlfire15]

Neither the custodial parent or the non custodial live with me. I am in the process of getting legal guardianship of him.

[girlfire15]

The child is related to me I am his great aunt.