McDonald, 25, was on the transfer list at Sixfields and has agreed a two-year contract with the Sky Blues.
He is Coventry's third signing following relegation from League One, after striker Marc McNulty and midfielder Michael Doyle.
"He is a quick, strong and aggressive centre-half, who can also read the game well," boss Mark Robins said.
Liverpool-born McDonald started his career at Manchester City's academy before joining the youth set-up at Stoke City.
He later went on to Oldham, Colwyn Bay, Nantwich, Hereford United and AFC Telford United, joining Northampton in 2015 and making 37 appearances for the Cobblers.
Find all the latest football transfers on our dedicated page.

The publication by German theologian Martin Luther, called On the Freedom of a Christian, dates back to 1520.
This was a year before he was excommunicated by the Pope for criticising the Catholic Church.
It includes around 50 notes written in red by Luther himself, indicating changes he wanted for a second edition.
The American who made the discovery, James Hirsten, said it gave an important insight into Luther's thinking at the time.
The annotated edition was found in The Humanist Library in Selestat, in the north-east of France.
Martin Luther launched the Reformation in Germany five centuries ago in response to what he said were excesses and abuses within the Church.
But his works, which also included Christian Liberty, To the Christian Nobility and On the Babylonian Captivity of the Church, turned him against many of the major teachings of the Catholic Church.
After his excommunication by Pope  Leo X in January 1521, Luther was declared an outlaw and a heretic by the Roman emperor at that time, Charles V.
He later went on to publish a complete translation of the bible into German, which contributed to the spread and development of the German language.

The Buccaneers thrilled the home fans by taking the lead through Thamsanqa Gabuza in the 36th minute.
He fired in a fierce acute-angled shot past Zied Jebali, who started after first choice goalkeeper and captain Aymen Mathlouthi failed a fitness test.
Of course we wanted to keep a clean sheet at home and a lapse of concentration gave Etoile a late equaliser
Pirates were lucky to be ahead at half-time after Iheb Msakni had a goal ruled offside and star Algeria-born striker Baghdad Bounedjah and Hamza Lahmar went close.
Etoile's quest for an equaliser paid off as captain and centre-back Ammar Jemal slammed a loose ball beyond goalkeeper Felipe Ovono from close range in the 87th minute to silence most of the 30,000 Soweto crowd.
Speaking after the match, Jemal told reporters what his equaliser meant to him.
"I think it is the best goal of my life," Etoile's captain said.
Despite conceding the late equaliser, Pirates coach Eric Tinkler said that the "destiny of the trophy remains wide open."
"We neither gained nor lost anything after this result," Eric Tinkler said.
"Of course we wanted to keep a clean sheet at home and a lapse of concentration gave Etoile a late equaliser. I thought we defended well until then.
"Etoile are a good team - well organised defensively with some big, strong boys," Tinkler added.
But the coach said he was not happy with some of the opposing players' tactics.
"Some of them dived so much I thought they were swimming at the Olympics.
"What the draw means is that instead of them coming at us in Tunisia, we will have to go at them. Scoring in every away CAF match this season gives us confidence," said Tinkler.
That deciding match will be played at Stade Olympique in Sousse, Tunisia on Sunday 29 November.
The overall winners receive $660,000 and qualify for a one-off Super Cup match against African Champions League winners TP Mazembe in the Democratic Republic of Congo.
Coventry City have signed centre-back Rod McDonald from Northampton for an undisclosed fee.
[NEXT_CONCEPT]
A first edition of one of the most important works of the man who inspired the Protestant Reformation has been discovered in a library in France.
[NEXT_CONCEPT]
Orlando Pirates of South Africa conceded a late goal in Soweto to hand Etoile du Sahel of Tunisia a narrow advantage as they drew 1-1 in the first leg of the African Confederation Cup final.