Per IRS Publication 17 Your Federal Income Tax For Individuals, on page 27:

Age Test

To meet this test, a child must be:

• Under age 19 at the end of the year and younger than you (or your spouse, if filing jointly);
• A student under age 24 at the end of the year and younger than you (or your spouse, if filing jointly); or
• Permanently and totally disabled at any time during the year, regardless of age.

Example. Your son turned 19 on December 10. Unless he was permanently and totally disabled or a student, he doesn't meet the age test because, at the end of the year, he wasn't under age 19.

Child must be younger than you or spouse. To be your qualifying child, a child who isn't permanently and totally disabled must be younger than you. However, if you are married filing jointly, the child must be younger than you or your spouse but doesn't have to be younger than both of you.

Student defined. To qualify as a student, your child must be, during some part of each of any 5 calendar months of the year:

1. A full-time student at a school that has a regular teaching staff, course of study, and a regularly enrolled student body at the school; or
2. A student taking a full-time, on-farm training course given by a school described in (1), or by a state, county, or local government agency.

The 5 calendar months don’t have to be consecutive.

Full-time student. A full-time student is a student who is enrolled for the number of hours or courses the school considers to be full-time attendance.

School defined. A school can be an elementary school; junior or senior high school; college; university; or technical, trade, or mechanical school. However, an on-the-job training course, correspondence school, or school offering courses only through the Internet doesn’t count as a school.

Vocational high school students. Students who work on “co-op” jobs in private industry as a part of a school's regular course of classroom and practical training are considered full-time students.

Permanently and totally disabled. Your child is permanently and totally disabled if both of the following apply.

• He or she can’t engage in any substantial gainful activity because of a physical or mental condition.
• A doctor determines the condition has lasted or can be expected to last continuously for at least a year or can lead to death.

Note that any link in the information above is updated each year automatically and will take you to the most recent version of the document at the time it is accessed.