Dawson is currently CIO for internet retailing at Tesco, reporting to group CIO Mike McNamara. His start date will be "announced in due course", a spokesperson for M&S said.
"Carl has a wealth of IT experience from the retail industry and joins us from Tesco," Marc Bolland, M&S CEO told staff in an internal memo.
M&S's head of business solutions in its online business, Clifford Cohen, will act as interim IT director until Dawson begins his new role.
When he joins M&S, Dawson will report to the chief finance officer, which Stein also did. There is currently an interim CFO at the retailer, after Alan Stewart left to join Tesco.
At a shareholder meeting just before his departure was announced, Stewart likened the problems that M&S has had with its new website to being "a bit like going to the supermarket for milk, they've moved it and you can't find it immediately".
A search for a new CFO is ongoing, said M&S.
M&S reported a fall in online sales recently mainly due to its new £150 million ecommerce site taking time to settle in after the retailer migrated it from Amazon to its own, in-house platform.
However, Tesco is experiencing its own share of troubles. The UK's largest supermarket's CEO, former CIO Philip Clarke, resigned this week following yet another profit warning. He is being replaced by Unilever's marketing lead Dave Lewis.