Moore, who is 6ft 5ins, scored 10 goals in 21 league appearances this season for Rovers and Torquay, where he had a brief loan spell earlier this term.
The 24-year-old has penned an 18-month deal at Portman Road.
Spence, 26, has signed to the end of the season having been without a club since leaving MK Dons in the summer.
The former West Ham defender played 80 times for the Dons after joining on a full-time contract, following two separate loan spells.
Both are unavailable for Ipswich's FA Cup third-round replay at Lincoln on Tuesday as they were not registered before the original tie.
Ipswich Town boss Mick McCarthy confirmed on Saturday to BBC Radio Suffolk he was still searching for another striker despite signing Moore, having previously had an approach turned down by Preston for Jordan Hugill.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.

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The 25-year-old batsman died when he was  by a short-pitched delivery in Sydney.
The incident was described as a "freak" by medical experts.
Hampshire-based manufacturer Masuri has given the BBC an exclusive look at its prototype helmet, which features extra protection at the rear.
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Batting for South Australia in a Sheffield Shield game against New South Wales in Sydney, Hughes was hit by a bouncer from Sean Abbott.
The batsman, who was wearing a Masuri helmet, collapsed immediately and died in hospital two days later.
After his death, the company began investigating a possible redesign and have introduced a "stemguard", a device made of foam and a rubber-like compound that clips onto the back of a helmet.
According to the company, Masuri provide "the most widely used helmet in Professional Cricket".
Design consultant Alan Meeks believes it will be both light and robust enough to prevent serious injury
"This arrangement of the foam and honeycomb gives as much protection as a hard helmet," he told BBC Sport.
"Even though it moves around and will touch the player when the ball hits them, it will absorb a significant amount of energy."
The International Cricket Council, which governs the game, has raised its recommendations for helmet safety standards in recent years.
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However, in response to the growth in popularity of the 20-over format of the game, which encourages a greater range of strokes and a riskier style of batting, research and development had focused on protecting a batman's face.
The death of Hughes, who played 26 Tests for Australia, changed things.
"That tragic event definitely had an impact on the public," said Masuri's managing director, Sam Miller.
"I don't think there was a helmet on the market which would have protected Phillip.
"There had been some talk of protection to that area in the past, but it had been a footnote."
The "stemguard" has been tested extensively in a laboratory while it awaits production. Masuri say they have consulted international cricket boards throughout the design process.
A patent for the product is pending but its introduction in matches will depend on players' desire to wear the redesigned helmets.

Clubs are required to provide accurate details of training sessions and player whereabouts so that they are available for testing at all times.
City have allegedly failed to ensure its information was accurate on three occasions.
The FA has a 'three strikes' policy and the most likely punishment is a fine.
It is understood the information was not updated following a change to training routines.
BBC Sport's Simon Stone
The fact City have accepted the charge is not a surprise.
Doping is a word that attracts big headlines and they are even greater when it is attached to one of the world's leading football clubs.
However, as I understand it, the three breaches of the whereabouts rule were relatively low level.
Clubs are responsible for a number of teams - senior, women, under-23 - and one infringement by each would be enough to trigger a charge.
Still, it is slightly embarrassing for the Blues, who are likely to receive some sort of fine.
Ipswich Town have signed striker Kieffer Moore from National League side Forest Green for an undisclosed fee and former MK Dons defender Jordan Spence.
[NEXT_CONCEPT]
A British-based firm has designed a cricket helmet aimed at preventing another tragic death like that of Australian Phillip Hughes last year.
[NEXT_CONCEPT]
Manchester City have accepted a Football Association anti-doping charge after failing to notify officials of player whereabouts for drugs testing.