Can I claim a college student who is 26 years old as a dependent if he is away all year at a university?

26?  Did he have less than $4050 in income for 2017?

yes

Maybe.  You can no longer claim him as a "Qualifying Child" because he was over age 24 at the end of the year.

However, if he makes less than $4,050 and you provide more than half of his support, you may be able to claim him as a "Qualifying Relative."

To be considered a "Qualifying Relative" a person has to meet these requirements:

1. Not a qualifying child - He is too old to be a qualifying child, so you're OK here.
   
2. Member of household or relationship test – Since he is away at school, this is still considered living with you.
3. Gross income test - To meet this test, a person's gross income for the year must be less than $4,050.  Gross income is all income in the form of money, property, and services that isn't exempt from tax.
4. Support test - To meet this test, you generally must provide more than half of a person's total support during the calendar year.  You figure whether you have provided more than half of a person's total support by comparing the amount you contributed to that person's support with the entire amount of support that person received from all sources. This includes support the person provided from his or her own funds.   

Another factor to consider is health insurance. If you do claim your student after 26 any credits they may qualify for under ACA will be based on your income. So the tax deduction may not be worth the higher cost for health insurance.

-Robert