Final solution:
<Style x:Key="DataGridContentCellCentering" TargetType="{x:Type DataGridCell}">
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type DataGridCell}">
<Grid Background="{TemplateBinding Background}">
<ContentPresenter VerticalAlignment="Center" />
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>