The recently launched company, which employs 35 staff and has a £4m turnover, provides data collection, management, analysis, campaign development and implementation across multiple channels.
Simpson's new role as chairman will include driving the development of the agency's concept of high-definition marketing.
Simpson said: "The direct marketing industry is long overdue a wake-up call. Consumers have got smarter and channels of communication have fragmented, but marketers have lost sight of the individual amongst all of the data that they collect."
"Data Lateral puts marketing directors back in control of this increasingly complex environment with a high-definition marketing philosophy that will shake up the industry."
Simpson joined Midland Bank from Cambridge University in 1970. He was involved in developing the business strategy that led to the launch of First Direct in 1989 and became the bank's commercial director in 1992, a role in which he stayed for 12 years.
In 2004, Simpson was appointed head of UK marketing for HSBC, first direct's parent company. In May last year he stepped down and handed the role over to former HBOS head of customer and brand strategy, James Boulton, who started in November.
Ruaraidh Thomas, managing director of Data Lateral, said of Simpson: "He will help us turn Data Lateral into a leader as new breed of marketing company able to wrap technologies and data round customers with real creativity."
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