Mr Devaney is currently on a one-year rolling contract paying him annual salary and fees of pounds 350,000 a year, with extra bonus and pension payments.
The news came as speculation continued that Mr Devaney is the front man for a City-led consortium seeking to invest in the UK energy market.
Eastern Group said that Mr Devaney is seeking "fresh challenges, but we don't know what they are". One City rumour is that Mr Devaney is involved with a consortium mulling a possible pounds 7bn takeover bid for National Power, Britain's largest power generator, or seeking to buy power stations from National Power and PowerGen, which are expected to be broken up by the electricity regulator, Stephen Littlechild.
Eastern yesterday described the idea of a Devaney-led bid for National Power as "fanciful". National Power shares, which had risen on the speculation, yesterday fell by 2.5p to 523p.
Texas Utilities said that it had "reluctantly" accepted Mr Devaney's resignation, effective from 14 September, and said he would remain as a non-executive chairman and consultant to the group.
The statement said that the search for a successor would begin immediately and that Mr Devaney would help with that search.