Balding will take over from former footballer Tony Adams MBE, who is halfway through his one-year term in the honorary and ceremonial role.
Smith, the chief executive of Hull Kingston Rovers, will succeed Doncaster’s Carl Hall, also next summer, as the longest-serving member of the rugby league council.
Both appointments were ratified at Tuesday's RL council meeting at Emerald Headingley Stadium in Leeds.
Balding will be in post for two years from July 2020-22 and Smith from July 2020-21.
Balding said: “I am so proud to be asked to help promote the wonderful sport of rugby league.
"As I know from my time presenting the game and following it as a fan, it is full of tradition and history, but has a truly modern outlook. It’s going global with teams from Europe and Canada alongside the great traditional clubs and I think this is a really exciting time. "
Balding added: “I am particularly thrilled to be involved as we head to the Rugby League World Cup in 2021, the first major international sports event to embrace the men’s, women’s and wheelchair tournaments together.
"Rugby league does great work in its communities and leads the way with inclusion in sport and the growth of women’s rugby league in particular has been wonderful to watch.
“I have loved it since I watched it as a child with my grandmother who used to tell me 'now this is a proper sport’. I realised how true that was when I started presenting it for the BBC and have always admired the team spirit, friendly atmosphere and strong moral code that it encourages.
"I have always felt welcomed by the rugby league family and I can’t wait to spend more time with the sport’s many characters.
“I am honoured to be the next president of the Rugby Football League and will promote rugby league nationally and internationally.
"I will be supporting the current RFL president Tony Adams as he continues his great work to champion the sport and look forward to taking up my role in summer 2020.”
Smith has been chief executive of Hull KR since September 2010 and was also involved with community club Skirlaugh.
He said: “I see this as a great honour, for myself and also to represent Hull Kingston Rovers in the role.
"It’s been filled by so many distinguished names in the past and doubtless will be in the future. I love the game and I’m really looking forward to working alongside Clare Balding and putting my heart and soul into this role.”
RFL chairman Simon Johnson said: “Our sport has been enhanced by having so many distinguished bearers of the offices of president and vice-president - Tony Adams and Carl Hall are proving to be superb office holders this year.
“We are delighted that the members of the rugby league council have agreed wholeheartedly with our recommendation that Clare Balding and Mike Smith will be fitting successors in 2020-21.
“Clare’s profile and popularity, coupled with her authentic love of the sport, will be a huge asset to rugby league as we look forward to hosting three World Cups – men’s, women’s and wheelchair – in England in 2021.
“Mike has given outstanding service to Hull Kingston Rovers in the professional game and also has a deep knowledge of the community game from his previous roles with Skirlaugh.
“Both will bring tremendous value to our sport in our 125th year. I look forward to welcoming them to their roles in the summer.”
Three new names have been added to the RFL's role of honour: former vice-president Pat Crawshaw, for outstanding contribution to the women’s and community game, His Honour Peter Charlesworth, who stepped down from the RFL operational rules tribunal this month after 26 years' service and Stuart Sheard, a former schoolteacher who has worked in the professional game for clubs including Sheffield Eagles and Huddersfield Giants.