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He is joined by Central Districts batsman Will Young and Wellington wicketkeeper Tom Blundell in being offered Black Caps contracts.
New Zealand Cricket yesterday announced the list of 20 contracted players for 2019-2020.
Fast bowler Adam Milne, batsman George Worker and all-rounder Corey Anderson have dropped out from last season's group.
Milne has been plagued by injury during the past 12 months and has not played a one-day international for New Zealand since October 2017.
He did play a couple of twenty20 games for the Blacks Caps in November but was overlooked for a contract.
Anderson has also been held back by injury and health problems and missed out on a spot in the World Cup squad.
His spot has effectively gone to Neesham, who has battled back from injury and form issues
He struck some delightful form with the bat this season, although his bowling is still of dubious value at the top level. However, he appears to have pulled ahead of Colin de Grandhomme as the country's No1-ranked all-rounder in one-day cricket.
"Jimmy had a very good season and made excellent progress with Wellington, New Zealand A and the Black Caps," national selector Gavin Larsen said.
"He's made every post a winning one."
Young gets a central contract for the first time after impressing for his province. He is firmly entrenched as the country's No1 back-up top-order batsman.
Otago's Hamish Rutherford is challenging for that spot, though. He is fresh from three centuries for his county side and might be an outside chance for the World Cup should injury strike .
"Will receives an offer on the basis of the sheer weight of runs he scored last season, both for New Zealand A and the Central Stags," Larsen said.
"He would've received his first test cap in March had it not been for the match being cancelled because of the Christchurch attack."
Blundell, who was a surprise inclusion in the World Cup squad, has picked up his first Black Caps contract as well.
He announced his presence when he scored a test century on debut while filling in for regular test keeper BJ Watling late in 2017.
No Otago cricketers have been offered national contracts.
The top-ranked contracted player earns a base fee of $239, 540 which drops in increments.
The bottom payment for players ranked 18-20 is $101,500.
Players also have the opportunity to pick up match fees of $9000 per test, $4000 per ODI and $2,500 for T20 matches.