The South African pair will line up for the Ageas Bowl outfit against Sussex Sharks in their Vitality Blast showdown at Hove on Wednesday night (7pm).
Morris took a wicket and scored 11 not out on his debut for James Vince’s side in the two-wicket defeat to Kent Spitfires on Sunday.
The pace-bowling all-rounder took 13 wickets for South Africa in the World Cup, won by England earlier this month.
He could not prevent a dismal group-stage exit for the Proteas, who lost five of their first seven games.
But Rossouw is confident Morris will put that disappointment quickly behind him and fire-up Hampshire’s challenge for a place at Finals Day.
The batsman said: ‘The better players put things behind them more easily, forget about failures and focus on what is next.
‘He is a very good professional and he will definitely put the World Cup behind him.
‘I thought he bowled really well, though, and comes into this tournament in good form.
‘He can definitely hit a long ball and will strengthen our batting line-up immensely at six or seven.
‘I am really looking forward to seeing what he will give to Hampshire.
‘And I think the Ageas Bowl will suit him – especially his bowling.’
Hampshire, who were domestic T20 champions in 2010 and 2012, managed only two wins in the group stage last season.
Rossouw, who opened the batting alongside Aneurin Donald against Kent, is determined to help them hit back.
He said: ‘Goal number one is to win a trophy but if that doesn’t happen then we want to play good cricket and see how far we can go.
‘Last year was a disappointment. We underperformed.
‘We are one of the better sides when it comes to white-ball cricket and how we performed last year is nowhere near how good we are as a group.
‘There was also a little bit of bad luck, so hopefully that changes and we go a step further and reach the knockout stages.
‘Last season we didn’t complement each other well enough in the top order.
‘This time we have analysed to see where we can do better.’