Ms McDonald announced his departure from office on Saturday night over "inappropriate" past conduct which had been subject of an SNP investigation.
First Minister Nicola Sturgeon said that Ms Todd will begin her ministerial duties immediately, subject to approval by Parliament.
The First Minister said: “I am really pleased that Maree has agreed to take up the post of Minister for Childcare and Early Years.
“Improving the life chances of children and young people is at the heart of this Government’s agenda, so this is a crucial post. We want to make Scotland the best place in the world to grow up and are taking forward a range of actions to achieve this.
“The importance of early years development simply cannot be overstated, which is why my government is putting so much emphasis on doing all we can to ensure youngsters across Scotland can reach their full potential."
Ms Todd has only been an MSP for 18 months after being elected in last year's Holyrood election and said she was "honoured" to be appointed.
She added: "The early years are so crucial in shaping Scotland’s next generation. A lot of great work has already been done and I am really looking forward to continuing to take forward policies like the Baby Box, the commitment to almost doubling entitlement to free early learning and childcare hours and leading celebrations for the Year of Young People 2018.
“I am relishing getting started and helping make a difference to the lives of all children in Scotland.”