BSD is a very permissive license. It allows many things, including redistributing it under different conditions, including as closed source. The only thing to respect, are the conditions of the BSD.
To dive into this, there are different variants of the BSD-license. The original 4-clause-BSD, a three-clause-BSD without the advertisement-clause and a two-clause-variant that only keeps the first two clauses. The original BSD reads as follows:
Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
in binary form must reproduce the above copyright notice, this list of
conditions and the following disclaimer in the documentation and/or
other materials provided with the distribution.
materials mentioning features or use of this software must display the
following acknowledgement: “This product includes software developed
by the University of California, Berkeley and its contributors.”
Neither the name of the University nor the names of its contributors
may be used to endorse or promote products derived from this software
without specific prior written permission.
So you need: to keep the original copyright-notice (including the authors of the original work), include the BSD-license with your distribution and the disclaimer about Warranty (that I omitted) for clause one and two (that only decide this for source and binary form). Clause 3 asks that all advertisement material includes this notice and clause four simply asks not to misuse the name of the university. This has to be followed. The variants simply omit clause 3, or clause 3 and 4.
The second thing: are these conditions compatible with the GPL. The result is: the original BSD isn't because of the advertisement-clause. The two variants omitting said clause are compatible .
Tl;DR: You cannot with original BSD, but can with 3-clause- and 2-clause-BSD.