Let
q
q
be a power of an odd prime, and
F
q
[
T
]
\mathbb {F}_q[T]
be the ring of polynomials over a finite field
F
q
\mathbb {F}_q
of
q
q
elements. A quadratic form
f
f
over
F
q
[
T
]
\mathbb {F}_q[T]
is said to be regular if
f
f
globally represents all polynomials that are represented by the genus of
f
f
. In this paper, we study definite regular quadratic forms over
F
q
[
T
]
\mathbb {F}_q[T]
. It is shown that for a fixed
q
q
, there are only finitely many equivalence classes of regular definite primitive quadratic forms over
F
q
[
T
]
\mathbb {F}_q[T]
, regardless of the number of variables. Characterizations of those which are universal are also given.