The tough-tackling midfielder is being released by Spurs after more than a decade at the club. Howells is out of contract and wanted to stay at White Hart Lane for a further three years, but the club were not prepared to meet his demands.
The Saints manager, Dave Jones, moved in to match 30-year-old Howells' terms and he will sign a three-year deal once his Tottenham contract expires on 30 June.
Howells' agent, Phil Graham, said: "David has agreed to join Southampton and will officially move to The Dell once his contract at Spurs expires."
The Dundee manager, Jocky Scott, has appointed the Dunfermline coach, Jimmy Bone, as his No 2 at Dens Park. Bone had been working without a contract at East End Park.
"I needed someone experienced and respected who knows the Premier Division, because it's vital we consolidate this season," Scott said. Dundee won the First Division last season.
Bone is a former manager at Airdrie, St Mirren and East Fife, and has also been in charge of the Zambian national side. Scott added: "Jimmy has played, managed and coached at the highest level. He'll be a great acquisition for Dundee."
Pat Nevin believes his former Scotland colleague Ian Durrant will feel at home at Kilmarnock after completing his move from Rangers.
"They are a brilliant bunch of guys and it is a fun place to play at," said Nevin, the former Scotland winger who moved to Kilmarnock last summer from Tranmere Rovers.
"In all the years I have been playing I have never known a more relaxed atmosphere apart from with the Scotland squad," Nevin added.
"Ian might be a little bit unsure of himself at first after such a long time at Rangers. But he is a confident player and a big personality and I am sure he will soon settle in without any difficulty."