We study the truncated shifted Yangian
Y
n
,
l
(
σ
)
Y_{n,l}(\sigma )
over an algebraically closed field
k
\Bbbk
of characteristic
p
>
0
p >0
, which is known to be isomorphic to the finite
W
W
-algebra
U
(
g
,
e
)
U(\mathfrak {g},e)
associated to a corresponding nilpotent element
e
∈
g
=
g
l
N
(
k
)
e \in \mathfrak {g} = \mathfrak {gl}_N(\Bbbk )
. We obtain an explicit description of the centre of
Y
n
,
l
(
σ
)
Y_{n,l}(\sigma )
, showing that it is generated by its Harish-Chandra centre and its
p
p
-centre. We define
Y
n
,
l
[
p
]
(
σ
)
Y_{n,l}^{[p]}(\sigma )
to be the quotient of
Y
n
,
l
(
σ
)
Y_{n,l}(\sigma )
by the ideal generated by the kernel of trivial character of its
p
p
-centre. Our main theorem states that
Y
n
,
l
[
p
]
(
σ
)
Y_{n,l}^{[p]}(\sigma )
is isomorphic to the restricted finite
W
W
-algebra
U
[
p
]
(
g
,
e
)
U^{[p]}(\mathfrak {g},e)
. As a consequence we obtain an explicit presentation of this restricted
W
W
-algebra.