Reflecting on her tenure since Labour returned to power in 2024, Stevens called her service "a privilege and an honour."
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She wished the new prime minister and her successor well, adding they would "do a great job, alongside our new Welsh Labour leader Ken Skates, in delivering for the people of Wales."
Welsh First Minister Rhun ap Iorwerth urged Burnham to "turn his commitment to devolution into action" during their initial phone call.
He called for devolved control over policing, justice, rail, and the Crown Estate, hoping for a "positive and productive relationship."
A Downing Street spokesperson said Burnham sought a "collaborative, practical and pragmatic" relationship with devolved leaders, adding that working together could achieve "deeper devolution."
Plaid Cymru Westminster leader Liz Saville Roberts described the role of Welsh secretary as an "anachronism" but noted her party's Senedd election victory in May provided a "clear mandate" for discussions on devolving key powers.
Gower MP Tonia Antoniazzi reflected on political changes following May's results, characterizing the period as a "brutal 24 hours."
She said, "I think people saw Reform as either being a protest vote.
A lot of our voters went to vote Reform or Plaid Cymru, and there has been a change in the Senedd and we accept that."
In other government changes, Vale of Glamorgan MP Kanishka Narayan was named minister for artificial intelligence with cabinet attendance.
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Torfaen MP Nick Thomas-Symonds stepped down as chief EU negotiator, calling his service "an honour to have a role at the centre of government" and stating that UK-EU relations were in a "far better state than when I took up the role in July 2024."
